Unit3A_KoscielnyD

toc = Lesson 26 =

Mass on a Spring Lab
Question: What is the relationship between the force that a spring exerts on a mass and the distance the spring stretches? Hypothesis: They are directly proportional when the object and spring are at rest (while they are accelerating the forces are unequal). Data: ...for spring lab:
 * || Trial # || mass (kg) || distance (m) |||| weight (N) || Trial # || mass (kg) || distance (m) || weight (N) ||
 * Spring 1 || 1 || 0 || 0 || 0 || Spring 2 || 6 || 0 || 0 || 0 ||
 * ^  || 2 || 0.015 || 0.049 || 0.147 ||^   || 7 || 0.2 || 0.018 || 1.96 ||
 * ^  || 3 || 0.03 || 0.098 || 0.294 ||^   || 8 || 0.4 || 0.039 || 3.92 ||
 * ^  || 4 || 0.045 || 0.146 || 0.441 ||^   || 9 || 0.6 || 0.06 || 5.88 ||
 * ^  || 5 || 0.06 || 0.198 || 0.588 ||^   || 10 || 0.8 || 0.082 || 7.84 ||

...for period vs mass
 * Trial# || Mass (kg) || Period (s) ||
 * 1 || 0.025 || 0.61 ||
 * 2 || 0.035 || 0.71 ||
 * 3 || 0.045 || 0.797 ||
 * 4 || 0.055 || 0.862 ||

Graphs:

Calculations: Weight= m*g Weight= .02*9.8 Weight= 1.96 Period= average time collected for 10 bounces / 10 Period= 8.62/10 Period=0.862

Conclusion + Error: What is the relationship between the period of oscillation & the mass? The more mass, the longer the spring will oscilate because the larger masses have greater inertia. What are some sources of error for this lab? We could have measured the initial and other displacements of the spring imprecisely for the first part of the lab and reaction time could have been off by a little for the period part of the lab.

Hooke's Law: Spring Force= -k (delta)x

Waves
Mechanical Waves- require a medium (medium= what carries the wave, transferring the energy, must be made of interacting particles) to travel in - transverse wave: the particles oscilate perpendicular to the direction of the wave travel - longitudinal- the particles oscillate parallel to the direction the wave travels - Wave Properties Electromagnetic Waves- does not require a medium
 * crest- maximum displacement
 * trough- minimum displacement
 * displacement in graph
 * region of compression- particles are close together
 * rarefaction- particles are farther apart, less dense, low pressure region
 * pressure and distance or time in graph
 * wavelength- the distance between a point on a wave and the same point on the next wave (constant)
 * amplitude- distance from equilibrium to crest or trough (constant)
 * period- time for one complete cycle (one wavelength of time)
 * speed of a wave: d/t, wavelength/period
 * frequency- how many waves pass in one sec, reciprocal of the period
 * reflection- when a wave encounters an obstacle and bounces off it (angle of incidence is always equal to the angle or reflection)- waves are inverted at a fixed end and come back non-inverted for a moveable end (rope to string is moveable, string to rope is fixed)
 * refraction- a wave encounters a boundaries but rather than bouncing off, it changes it's direction because of change in wave speed
 * __**wave speed is completely and only dependent on the medium it is and is constant**__ within a medium, if increase one of the variables the other decreses
 * diffraction- encounters an obstacle or opening and the wave bends around to fill the space behind the opening, the bigger the opening, the less diffraction, the shorter the wavelength, the less diffraction
 * interference- two or more waves are at the same place at the same time, their energies (amplitude) temporarily sum

= Homework = **Reading Summary:** __Vibrational Motion__ There are several key terms to describe an object's vibration; **the resting position** is when the object is in a state of equilibrium, **forced vibration** is when an object is pushed in to motion from rest, and **damping** is the dissipation of energy of on object restoring it to rest due to **restoring forces**.

__Properties of Periodic Motion__ __Pendulum Motion__ Weight and tension are the forces in pendulum motion, changing potential energy to kinetic energy and back causing the velocity to be ever changing.
 * Periodic motion** will always make a sinusoidal p-t graph; its size is based on **period** (time of one cycle) or **frequency** (cycles per one second) and **amplitude** (displacement to max or min).

__Motion of a Mass on a Spring__
 * Hookes law** states that the amount a spring is extended is proportional to the force it has, so **Fspring = -k•x** ; however, direction of this force depends on whether the spring is compressed or extended; the period of the spring can be determined using **T = 2•π•(m/k)0.5**.

= Lesson 27 = = Slinky Lab =
 * Procedure:**
 * //Part I// – Marking the floor**
 * 1) Place strips of masking tape approximately .75m long on the floor at 0.0 m, 5.0 m and 10.0 m.
 * 2) **//Mark//** and **//label//** a heavy ink/pencil line in the **//center//** of the tape at 0m.
 * 3) Mark and label lines 10.0 cm, 20.0 cm and 30.0 cm to the **//left//** and **//right//** of your center mark on each.


 * //Part II// – Making a transverse pulse**
 * Stretch your spring between the 0.0 m and 5.0 m tape marks on the floor with the rope loops around your wrist being located about 0.5 m beyond the tape marks on the floor.
 * Move your hand back and forth at right angles to the stretched spring until you can produce a pulse that travels down only one side of the spring (that is, the bump on the spring due to the pulse is only on the right or left side of the spring).
 * Send a pulse down the spring that has an **amplitude** of **10.0 cm**. Have the third member of your group time the pulse as it travels from 0.0 m to 5.0 m.
 * Repeat steps #8-11 for pulses having amplitudes of 20.0 cm and 30.0 cm.
 * Repeat steps # 8-11 for 10-m distance.
 * **//Table 1 - Speed of pulses (Spring A) Slinky //** ||
 * |||||| **5.0 meter total distance ** |||||| **10.0 meter total distance ** ||
 * **Amplitude (cm) ** || **//20 //** || **//30 //** || **//40 //** || **//20 //** || **//30 //** || **//40 //** ||
 * **Trial 1 time (s) ** || 0.128 || 0.134 || 0.137 || 1.0 || 1.16 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">1.25 ||
 * **<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">Trial 2 time (s) ** || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.128 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.121 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.125 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">1.03 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">1.13 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">1.28 ||
 * **<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">Trial 3 time (s) ** || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.132 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.138 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.14 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">1.06 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">1.16 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">1.22 ||
 * **<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">Avg.time (s) ** || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.129 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.131 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.134 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">1.0 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">1.15 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">1.25 ||
 * **<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">Distance (m) ** || **//<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">5 //** || **//<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">5 //** || **//<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">5 //** || **//<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">10 //** || **//<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">10 //** || **//<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">10 //** ||
 * **<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">Avg. Speed (m/s) ** || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">38.66 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">38.17 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">37.31 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">9.71 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">8.70 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">8 ||


 * Repeat steps # 8-11 for a more tightly coiled spring.
 * **//<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 21.3333px;">Table 2 - Speed of pulses (Spring B) Snakey Spring //** ||
 * |||||| **<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 18.6667px;">5.0 meter total distance ** |||||| **<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 18.6667px;">10.0 meter total distance ** ||
 * **<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">Amplitude (cm) ** || **//<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">20 //** || **//<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">30 //** || **//<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">40 //** || **//<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">20 //** || **//<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">30 //** || **//<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">40 //** ||
 * **<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">Trial 1 time (s) ** || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.47 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.53 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.5 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.56 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.59 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.72 ||
 * **<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">Trial 2 time (s) ** || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.5 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.54 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.5 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.59 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.68 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.66 ||
 * **<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">Trial 3 time (s) ** || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.53 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.47 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.5 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.59 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.66 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.69 ||
 * **<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">Avg.time (s) ** || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.50 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.51 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.50 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.58 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.64 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.69 ||
 * **<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">Distance (m) ** || **//<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">5 //** || **//<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">5 //** || **//<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">5 //** || **//<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">10 //** || **//<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">10 //** || **//<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">10 //** ||
 * **<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">Avg. Speed (m/s) ** || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">10 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">9.74 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">10 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">17.24 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">15.54 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">14.49 ||

- The logitudinal pulse travels along the slinky and back just as the transverse pulse did, only parallel rather than perpendicular. - it is difficult to achieve no perpendicular motion along with the parallel motion, but there is little enough perpendicular motion that the parallel motion is clear.
 * //Part III// – Making a longitudinal pulse**
 * 1) Make sure that the rope loops at the end of the springs are around your wrist. With your free hand, grasp the stretched spring about a meter from one end. Pull the meter of spring together toward yourself and then release it, being careful not to let go of the fixed end with your other hand! Another way to do this is to push the spring towards your lab partner and quickly bring it back to your original position.
 * 2) Repeat several times. Note several observations:

The speed of the waves is similar through the different amplitudes.
 * Discussion Questions**
 * How do the speeds of the waves compare for the 3 different amplitudes of the 5.0 meter distance?

It was not supposed to change, though it did a little due to experimental error.
 * Did amplitude influence the speed of the waves for the 5.0 meter distance?

The data got a little larger due to experimental error, but the actual speed did not.
 * How do the speeds of the waves compare for the 3 different amplitudes of the 10.0 meter distance?

The speed of the waves is similar through the different amplitudes.
 * Did amplitude influence the speed of the waves for the 10.0 meter distance?

The 10 meter was faster in snakey but slower in slinky.
 * How do the speeds of the waves compare for the 5.0 meter and 10.0 meter distances?


 * What changed when you measured the time for 10-m vs. the 5.0-m distance? Choose as many as apply.
 * **The medium changed.**
 * **The wavelength changed.**
 * **The speed changed.**
 * The frequency changed.

It differed between the lengths because the mediums differed. Snakey was faster with 10m and Slinky was faster with 5m.
 * How do the speeds of the waves compare for the 2 different types of springs?

Longitudinal go straight along a medium, traverse waves go side to side.
 * What are some differences between the longitudinal and the transverse wave?

= Homework = **Reading Summary:** __Waves and Wavelike Motion__ Waves and wavelike things are everywhere.

__What is a Wave?__ A wave is an **energy transport phenomenon** caused by multiple **disturbances** that travel through the molecules of a **medium;** a **pulse** is a single disturbance.

__Categories of Waves__ Molecules in a **transverse** **wave** travel perpendicular to the direction of the wave, while molecules in a **longitudinal wave** travel parallel, and molecules in a **surface wave** follow a circular path; **mechanical waves** require a medium while **electromagnetic waves** can travel through empty space.

**Cartoon:** image: http://www.offthemarkcartoons.com/cartoons/1996-01-13.gif website: http://offthemark.com/search-results/key/slinky/

image: http://cp.home.agilent.com/upload/cmc_upload/cartoon_VIBRTN3-lg.gif website: http://www.leapsecond.com/notes/cartoons.htm

Image: http://cp.home.agilent.com/upload/cmc_upload/cartoon_relax3.gif Website: http://www.leapsecond.com/notes/cartoons.htm

= Lesson 28 =

Adding Transverse Waves
node: point that always stays the same when waves are of equal amplitude anti-node: point that goes up and down the most

Transverse Standing Waves on a String Lab
<span style="font-family: 'Century Schoolbook','serif';">To determine the relationship between the number of harmonics, the frequency of the source, and the wavelength of transverse waves traveling in a stretched string.
 * <span style="font-family: 'Century Schoolbook','serif'; font-size: 18.6667px;">Purpose: **

The larger the number of harmonics, the greater the frequency, the smaller the wavelength.
 * <span style="font-family: 'Century Schoolbook','serif'; font-size: 18.6667px;">Hypothesis: **

<span style="font-family: 'Century Schoolbook','serif';">Electrically driven oscillator; pulley & table clamp assembly; weight holder & selection of slotted masses; black Dacron string;
 * <span style="font-family: 'Century Schoolbook','serif'; font-size: 18.6667px;">Materials: **

<span style="font-family: 'Century Schoolbook','serif'; font-size: 18.6667px;">Procedure: > **<span style="font-family: 'Century Schoolbook','serif'; font-size: 18.6667px;">L = __7.19 m__ **
 * 1) <span style="font-family: 'Century Schoolbook','serif';">Set the frequency of the oscillator to zero. Set the amplitude to maximum.
 * 2) <span style="font-family: 'Century Schoolbook','serif';">Measure the length L of the string.
 * 3) <span style="font-family: 'Century Schoolbook','serif';">Dial up the frequency a little at a time until you acquire a standing wave. If you are careful, you should be able to get the fundamental. However, if you don’t, it’s okay… just record the correct number of antinodes along with the frequency.
 * 4) <span style="font-family: 'Century Schoolbook','serif';">Measure the wavelength.
 * 5) <span style="font-family: 'Century Schoolbook','serif';">Repeat for at least 7 different harmonics. These do not have to be consecutive.
 * 6) **//<span style="font-family: 'Century Schoolbook','serif'; font-size: 18.6667px;">Data Table 1: Changing harmonic number //**
 * **<span style="color: #000000; font-family: 'Century Schoolbook','serif'; font-size: 18.6667px;">n ** || **//<span style="color: #000000; font-family: 'Century Schoolbook','serif'; font-size: 18.6667px;">f //****<span style="color: #000000; font-family: 'Century Schoolbook','serif'; font-size: 18.6667px;">(Hz) ** || **<span style="color: #000000; font-family: 'Century Schoolbook','serif'; font-size: 18.6667px;">Measured **** l ****<span style="color: #000000; font-family: 'Century Schoolbook','serif'; font-size: 18.6667px;"> (m) ** || **<span style="color: #000000; font-family: 'Century Schoolbook','serif'; font-size: 18.6667px;">Calculated v (m/s) ** ||
 * <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">1 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">11.6 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">14.38 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">166.808 ||
 * <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">2 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">23.3 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">7.19 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">167.527 ||
 * <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">3 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">34.9 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">4.79 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">167.171 ||
 * <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">4 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">48 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">3.595 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">172.56 ||
 * <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">5 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">59.1 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">2.876 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">169.9716 ||
 * <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">7 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">82.2 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">2.054 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">168.8388 ||
 * <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">15 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">177.2 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">0.9587 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">169.88164 ||

> Measure the wavelength. > Repeat steps 6 & 7, changing the mass on the string 5 times.
 * 1) <span style="font-family: 'Century Schoolbook','serif';">Add mass to the end of the string and find the frequency that creates the fourth harmonic.


 * //<span style="font-family: 'Century Schoolbook','serif'; font-size: 18.6667px;">Data Table 2: Changing Tension //**


 * **<span style="color: #000000; font-family: 'Century Schoolbook','serif'; font-size: 18.6667px;">Mass Hanging (kg) ** || **<span style="color: #000000; font-family: 'Century Schoolbook','serif'; font-size: 18.6667px;">Tension in the string (N) ** || **//<span style="color: #000000; font-family: 'Century Schoolbook','serif'; font-size: 18.6667px;">f //****<span style="color: #000000; font-family: 'Century Schoolbook','serif'; font-size: 18.6667px;">(Hz) ** || **<span style="color: #000000; font-family: 'Century Schoolbook','serif'; font-size: 18.6667px;">Measured **** l ****<span style="color: #000000; font-family: 'Century Schoolbook','serif'; font-size: 18.6667px;"> (m) ** || **<span style="color: #000000; font-family: 'Century Schoolbook','serif'; font-size: 18.6667px;">Calculated v (m/s) ** ||  ||
 * <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">0.5 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">4.9 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">34.1 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">3.595 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">122.5895 ||  ||
 * <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">1 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">9.8 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">47.7 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">3.595 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">171.4815 ||  ||
 * <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">1.5 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">14.7 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">56.7 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">3.595 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">203.8365 ||  ||
 * <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">2 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">19.6 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">65.3 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">3.595 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">234.7535 ||  ||
 * <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">2.5 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">24.5 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">73.9 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">3.595 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">265.6705 ||  ||
 * <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">3 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">29.4 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">81 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">3.595 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">291.195 ||  ||
 * <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">3.5 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">34.3 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">88.1 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">3.595 || <span style="color: #000000; display: block; font-family: 'Century Schoolbook',serif; font-size: 18.6667px; text-align: right;">316.7195 ||  ||
 * <span style="font-family: 'Century Schoolbook','serif'; font-size: 18.6667px;">Calculations: **
 * <span style="font-family: 'Century Schoolbook','serif';">Calculate the speed of the wave for each harmonic. (SHOW A SAMPLE CALC!)
 * <span style="font-family: 'Century Schoolbook','serif';">Calculate the speed of the wave for each harmonic. (SHOW A SAMPLE CALC!)

T=w=m*g T=.5*9.8 T=4.9
 * <span style="font-family: 'Century Schoolbook','serif';">Calculate the tension in the string. (SHOW A SAMPLE CALC!)


 * <span style="font-family: 'Century Schoolbook','serif'; font-size: 18.6667px;">Graphs: **
 * <span style="font-family: 'Century Schoolbook','serif';">Make a graph of //f// vs. //n// for Data Table 1.




 * <span style="font-family: 'Century Schoolbook','serif';">Make a graph of f vs. l <span style="font-family: 'Century Schoolbook','serif';">for Data Table 1 **<span style="font-family: 'Century Schoolbook','serif'; font-size: 18.6667px;">. **

<span style="font-family: 'Century Schoolbook',serif; font-size: 19px; line-height: 28px;">
 * <span style="font-family: 'Century Schoolbook','serif'; font-size: 18.6667px;">Make a graph of f vs. T for Data Table 2.

<span style="font-family: 'Century Schoolbook','serif';">1. What is the name given to a point on a vibrating string at which the displacement is always zero? - node
 * <span style="font-family: 'Century Schoolbook','serif'; font-size: 18.6667px;">Discussion Questions: ***

<span style="font-family: 'Century Schoolbook','serif';">2. What is the name given to a point at which the displacement is always a maximum? - antinode

<span style="font-family: 'Century Schoolbook','serif';"> 3. How is the length of the string related to the wavelength for standing waves? - wavelength is longer as the string is longer- they are directly proportional

<span style="font-family: 'Century Schoolbook','serif';">4. What is the longest possible wavelength for a standing wave in terms of the string length? - Twice the length of the string.

<span style="font-family: 'Century Schoolbook','serif';">5. Use your graph to find the frequency for n = 20. (Try it. Does it work?) - yes, it works with all ns frequency= slope*n 20*11.805=236.1 Hz

<span style="font-family: 'Century Schoolbook','serif';">6. What is the relationship between the speed of the wave and the harmonic number? <span style="font-family: 'Century Schoolbook','serif';">-they are independent

<span style="font-family: 'Century Schoolbook','serif';">7. What is the relationship between the speed of the wave and the frequency? <span style="font-family: 'Century Schoolbook',serif;">- inversely proportional

<span style="font-family: 'Century Schoolbook','serif';">8. What is the relationship between the wavelength and the harmonic number? <span style="font-family: 'Century Schoolbook','serif';">- the greater n, the shorter the <span style="font-family: 'Century Schoolbook',serif;">wavelength

<span style="font-family: 'Century Schoolbook','serif';">9. What is the relationship between the wavelength and the frequency? - inverse square

= Homework = **Reading Summary:** __Traveling Waves vs Standing Waves__ The displacement-time graph of a **traveling wave** looks like a sine function until it hits another wave or an obstruction, when the wave is at a specific frequency, the waves bouncing off the obstruction will form a **standing wave pattern** with the identical waves going in the other direction, forming nodes and anti-nodes.

__Formation of Standing Waves__ The 'magic' frequency that makes the pattern is the point at which the wave bounces back at the exact opposite curve.

__Nodes and Anti-nodes__
 * Nodes**, due to interference, always have minimum displacement while **Anti-nodes** always have maximum displacement.

__Harmonics and Patterns__
 * Harmonics** are the number of anti-nodes achieved by certain standing wave patterns. (first harmonic=1 anti-node, second harmonic= 2 anti-node...)

__Mathematics of Standing Waves__ Use the following equation to determine values of the wave using given or experimental values.

= Lesson 29 =

Resonance + Standing Waves
Resonance = when the natural frequency of an object is reinforced by an external object, causing a standing wave to form= when something is forced to virate at its natural frequency
 * things naturally vibrate at their natural frequency unless you force them to do otherwise
 * when you reinforce the natural frequency it can vibrate so much it breaks (glass, a bridge)

Standing wave= a pattern created by the interference of a wave due to resonance
 * (nodes and anti-nodes not crests and troughs)
 * n= # of antinodes on a string
 * node= position of minimum amplitude
 * anti-node= position of maximum amplitude

Intro to Sound

 * sound is a wave of pressure (longitudinal wave) that travels through the air
 * pressure vs time (singe physical point) or pressure vs distance graph (single point in time)
 * amplitude= how much energy conveyed= correlates to loudness
 * Loudness= perception of amplitude
 * Pitch= perception of frequency
 * the denser the material, the faster the sound
 * steel is over 10X as fast as air

Doppler Affect

 * speed of sound does not change within a medium
 * Doppler Affect= the change of frequency due to the moving of the source
 * Sonic boom= when all the sound waves from the Doppler affect build up in front of the plane and then the plane croses

= Homework = **Reading Summary:** __Sound is a Mechanical Wave__ Sound is a **mechanical wave** and thus needs a medium through which to travel and cannot travel through the vacuum of space.

__Sound is a Longitudinal Wave__ Sound is a **longitudinal wave**; it is the **compression** and **rarefaction** of the medium (usually air).

__Sound is a Pressure Wave__ A sound wave is a **pressure wave** because it is made of areas of low and high pressure

---

__Pitch and Frequency__
 * Frequency**, measured in **hertz** (**1 Hertz = 1 vibration/second)** is percieved by the human ear as **pitch**; if the frequency is bellow the range of human hearing (20Hz) it is an **infrasound** if it is above the range of human hearing (20,000Hz) it is an **Ultrasound**. When two frequencies "fit"together well, they are a **constant**, consants make up the basic **intervals** in music. I.E.
 * < **Interval** ||< **Frequency Ratio** ||< **Examples** ||
 * < Octave ||< 2:1 ||< 512 Hz and 256 Hz ||
 * < Third ||< 5:4 ||< 320 Hz and 256 Hz ||
 * < Fourth ||< 4:3 ||< 342 Hz and 256 Hz ||
 * < Fifth ||< 3:2 ||< 384 Hz and 256 Hz ||

__Intensity and the Decibel Scale__ The **Intensity** of a sound wave, measured in **decibels**, is proportional to the energy used to vibrate the medium and inversely square proportional to the distance, the least intense noise the human ear can hear is **the threshold of hearing**.

__The Speed of Sound__ The speed a wave can travel through a medium is dependent on **elastic** **properties** that decide how easily an object can be deformed and **inertial properties** that determine and object's inertia (mass & density).

__The Human Ear__ The ear canal amplifies sounds, the eardrum vibrates and the stirrup transfers this to the inner ear where the cochlea measures the noise and tell the brain what to hear.

**Joke:** image: [] website: []

image: [] website: []

Image: http://imgs.xkcd.com/comics/resonance.png Website: http://xkcd.com/228/

= Lesson 30 =

More Sound
(sound travels faster in hotter matter)

Intensity= how much power a sound source emits and the rate at which the energy is delivered= quantitative measure of loudness I= P/A=(power/surface area)= watts/m^2 Intensity gets smaller b/c energy dissipates- spreads out over a greater area Surface Area= 4*pi*r^2 Intensity Level= **Decibels**= sound level Decibels are on a logarithmic scale Threshold of hearing= 0 dB Threshold of discomfort= 120 dB Threshold of pain= 130dB To difference between two things is 10 to the dB dif with the 0 knocked off

Resonance Tube Lab

 * Objective: ** What is the relationship between the length of a tube and its resonant frequencies?


 * Hypothesis:** the more length the tube has, the more resonance there will be.


 * Materials: ** Resonance tubes with length scale marked on the tube, audio generator, speaker, class thermometer.

1) Measure the room temperature of the air and record it in Data Table 1. If the thermometer in the room measures temperature in oF it is necessary to convert to oC. 2) Your teacher will assign you a frequency, between 300 and 800 Hz. Calculate the wavelength of this sound, using the speed from Step 1. 3) Calculate the theoretical length of the column of air in the closed tube of the first 5 harmonics. Circle the ones between 0 and 2.6 meters. 4) Set the audio generator to emit the frequency that has been assigned to you. Lower the volume (amplitude) so that it is just barely audible. 5) Set the speaker next to the open end of the resonance tube. Set the tube to the first calculated length. Adjust the length of the tube by moving the inner tube in small increments in or out, until you hear the sound at its maximum amplification. Record the adjusted lengths as the Measured. 6) Repeat the procedure for the other calculated lengths.
 * Experimental Procedure: **
 * // Part A: Closed Tube //**

Table A: Closed Tube


 * **<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">Frequency (Hz) ** || **<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">Harmonic Number ** || **<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">Length of tube – Calculated (Theoretical) (m) ** || **<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">Length of tube – Calculated (Expeimental) (m) ** || **<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">% Error ** || **<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">Abbsolute Difference ** || **<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">Length Width End Affect ** || **<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">% Error Adjusted ** ||
 * <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">650 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">1 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.1338 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.067 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">49.94% || <span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;"> 0.067 || <span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;"> 0.077 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">13.49% ||
 * <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">650 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">3 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.4015 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.3395 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">15.45% || <span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;"> 0.062 || <span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;"> 0.345 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">1.63% ||
 * <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">650 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">5 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.6692 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.601 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">10.20% || <span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;"> 0.068 || <span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;"> 0.613 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">1.93% ||
 * <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">650 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">7 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.9369 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.852 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">9.06% || <span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;"> 0.085 || <span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;"> 0.881 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">3.24% ||
 * <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">650 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">9 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">1.2046 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">1.123 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">6.78% || <span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;"> 0.082 || <span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;"> 1.148 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">2.20% ||
 * <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">650 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">11 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">1.4723 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">1.426 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">3.15% || <span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;"> 0.046 || <span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;"> 1.416 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.71% ||
 * <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">650 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">11 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">1.4723 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">1.426 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">3.15% || <span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;"> 0.046 || <span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;"> 1.416 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.71% ||


 * // Part B: Open Tube //**

7) Your teacher will assign you a frequency, between 300 and 800 Hz. Calculate the wavelength of this sound, using the speed from Step 1.

8) Calculate the theoretical length of the column of air in the open tube of the first 5 harmonics. Circle the ones between 1.3 and 2.6 meters. These are the harmonics that you will try to hear experimentally. NOTE: You cannot test lengths SMALLER than 1.3 m or BIGGER than 2.6 m. Caluclate bigger harmonics to substitute for those values less than 1.3 m.

9) Set the audio generator to emit the frequency that has been assigned to you. Lower the volume (amplitude) so that it is just barely audible.

10) Set the speaker next to the open end of the resonance tube. Set the tube to the first calculated length. Adjust the length of the tube by moving the inner tube in small increments in or out, until you hear the sound at its maximum amplification. Record the adjusted lengths as the Measured.

11) Repeat the procedure for the other calculated lengths.


 * Table B: Open Tube **


 * **<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">Frequency (Hz) ** || **<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">Harmonic Number ** || **<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">Length of tube – Calculated (Theoretical)(m) ** || **<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">Length of tube – Calculated (Expeimental)(m) ** || **<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">% Error ** || **<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">Abbsolute Difference ** || **<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">Length Width End Affect ** || **<span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;">% Error Adjusted ** ||
 * <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">650 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">5 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">1.33846154 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">1.371 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">2.43% || <span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;"> 0.033 || <span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;"> 1.226 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">11.86% ||
 * <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">650 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">6 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">1.60615385 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">1.491 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">7.17% || <span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;"> 0.115 || <span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;"> 1.493 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.16% ||
 * <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">650 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">7 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">1.87384615 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">1.75 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">6.61% || <span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;"> 0.124 || <span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;"> 1.761 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.63% ||
 * <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">650 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">8 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">2.14153846 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">2.021 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">5.63% || <span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;"> 0.121 || <span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;"> 2.029 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.38% ||
 * <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">650 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">9 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">2.40923077 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">2.275 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">5.57% || <span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;"> 0.134 || <span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;"> 2.296 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">0.93% ||
 * <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">650 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">10 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">2.67692308 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">2.514 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">6.09% || <span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;"> 0.163 || <span style="color: #000000; font-family: 'Times New Roman','serif'; font-size: 16px;"> 2.564 || <span style="color: #000000; display: block; font-family: 'Times New Roman',serif; font-size: 16px; text-align: right;">1.95% ||

From the data in part A, make a graph of //Lexp// vs. //n//. Add the second set of data from Part B onto the same set of axes. Create a trendline, seting the y-int = 0 and including the equation of the line and R2 value.
 * GRAPH: **

12) Calculate the speed of sound. V=331+.6T V= 331+.6(27.5) V=347.5
 * Calculations: **

13) Using your data in Parts A and B, calculate the Percent Error between the Experimental Lengths and the Theoretical Lengths. %error= |(theo-exp)/theo| %error= |(1.34-1.37)/1.34| %error=.022 error= 2.2%

<span style="font-family: 'Times-Roman','serif'; font-size: 16px;">Discussion Questions The antinode shifts more when the diameter is larger- it shifts by +.8d (open) or +.4d. (closed) Otherwise the sound does not come out at its full amplitude and sound loudest. L=0.125/n L=0.125/10 L=0.0125 L=0.253/n L=0.253/10 L=0.0253
 * For an ideal resonance tube, an antinode occurs at the open end of the tube. What characteristic of real resonance tubes slightly alters the position of this antinode?
 * Why must there be an antinode at the end of the resonance tubes?
 * How long would the closed tube have to be to get the 10th harmonic?
 * How long would the open tube have to be to get the 10th harmonic?
 * Draw a figure showing the fifth resonance in a tube //closed// at one end. Show also how the length of the tube L5,is related to the wavelength, λ.
 * Draw a figure showing the fifth resonance in an //open// tube. Show also how the length of the tube L5,is related to the wavelength, λ.

= Homework = **Reading Summary:** __Natrual Frequency__ When something is hit, it vibrates with its **natural frequency** the quality or **timbre** of the sound depends on what that frequency is

__Forced Vibration__
 * Forced vibration** is when a vibrating object makes an adjoining or interconnected object vibrate at the first objects frequency, when both objects have the same frequency this is a type of **resonance**.

__Standing Wave Patterns__ Standing wave patterns represent the lowest energy **vibrational modes of an object**, also forming **nodal and anti-nodal points**.

__Fundamental Frequency and Harmonics__ To find the frequency of different harmonics, just multiply the first harmonic/**fundamental frequency** by n.

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__Resonance__
 * Slip-stick friction** is a kind of friction that causes things to vibrate at sound wave frequencies.

__Guitar Strings__ Guitar strings vibrate the same as other strings.

__Open-End Air Columns__ A column of air is open at both ends, the harmonics are at half wavelengths and both ends of the tube must have anti-nodes.

__Closed-End Air Columns__ A column of air is closed at one end, the harmonics are at quarter wavelengths and the closed end must have a node while the open has an anti-node, making even harmonics impossible.

= Lesson 31 =

Sound Vocabulary
Reflection: Echo (long range) and Reverberation (less than 17 m away) Refraction: wave bends due to change in medium- sound bends due to layers of air warmness Diffraction: waves bend around obstructions into the open space, but there are shadow regions Interference: - Resonance in strings and tubes - Beats- two sounds that are almost identical interfere- the # beats/ second is the absolute value difference between the two frequencies- the interference happens in a regular and repeatng pattern -double source- two sources make sections of constructive and destructive interference

= Homework = **Cartoon:**

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