Experiment 11:
Mechanical Waves
Objective:
To visually observe the mechanical waves behavior
Equipment:
A computer with the Internet connection, a calculator (The built-in calculator of the computer may be used), a few sheets of paper, and a pencil
Theory:
Mechanical waves are two types: longitudinal and transverse. Longitudinal waves oscillate parallel to their propagation direction. Transverse waves oscillate perpendicular to their propagation direction. In this experiment, the fundamental behavior of waves will be studied.
Sound is a longitudinal wave that travels at a speed of v = 331m/s at STP conditions. A longitudinal wave is one that oscillates parallel to its propagation direction. The way an induced disturbance travels in a slinky is a longitudinal wave motion. At a frequency ( f ) that we speak or sing (Audio range: 200Hz – 2000 Hz), the wavelength ( λ ) of a sound wave is in the range of (150cm – 15cm ). This may be verified by using the wave speed formula:
v = f λ
Resonance of Sound Waves in Open and Closed Pipes
In music, a pipe open at both ends is called an open pipe, and a pipe open at one end only forms a closed pipe as shown below:
Figure 1
Maximum deviation from equilibrium called amplitude for a sound wave can only occur at the open ends of a pipe (if the pipe length is suitable). This is because of the fact that at an open end of a pipe, air molecules are free to oscillate back and forth. At a closed end air molecules are not free to perform oscillations. In other words, closed ends form nodes. Open ends can form antinodes if pipes have the right lengths for antinodes to occur.
The following figures show how maximum and minimum oscillations occur at open and closed ends for a certain wavelength at different tube lengths:
Figure 2
Note that, for simplicity, representation of transverse waves are used to show states of maximum and minimum oscillation at open and closed ends. Sound waves, however, are longitudinal and oscillate back and forth parallel to the tube length and not up and down as shown. These figures only indicate where maxima and minima occur.
As can be seen from the figures, the length of a pipe must be multiples of ( ¼ λ ) for maxima at the open ends to occur. In an open end pipe, if the length of the pipe is an even multiple of ( ¼ λ ), then the open ends are at maximum states of oscillation, and a load sound is heard. The pipe is said to be in resonance. In a closed end tube, the length of the pipe must be an odd multiple of ( ¼ λ ) for resonance to occur (See the above figures.)
Wavelength: Wavelength ( λ ) is defined as the distance from one peak to the next peak on a wave. Of course, in general, wavelength is the distance between two successive points on a wave that are in the same state of oscillation.
Frequency: Frequency ( f ) is the number of waves (full λs) generated per second.
Figure 3
Procedure:
Click on the following link: http://surendranath.tripod.com/Applets.html On the Applet Menu, hold the mouse on "Waves" and click on "Transverse Waves."
Fill out Table 1 below by answering the questions as you progress through different parts of this applet.
With the wave in "Progressive" mode,
1) Move the "Amplitude" bar on the applet once to minimum and once to maximum (Q_{1}). Give an estimate in (cm) of the minimum and maximum amplitude (Q_{2}). 1 in. = 2.54cm.
2) Set the frequency ( f ) to minimum. If the whole span of the applet is 24cm, what wavelength do you measure (Q_{3})?
3) Set the frequency ( f ) to maximum. If the whole span of the applet is 24cm, what wavelength do you measure (Q_{4})?
With the wave in "Pulsed Crest", observe the wave motion. Next, with the wave in "Pulsed Trough", observe the wave motion. The assumption is that you are observing a 24-cm segment of a string infinitely long through which a wave is passing. Why doesn't the wave return (Q5)? By return, it is meant "going leftward."
4) Change the mode to "String fixed at both ends." With the "Amplitude" at any position you want, set the frequency to minimum. Now, to your opinion, is there a wave moving to the right(Q_{6})? Is there a wave moving to the left (Q_{7})? Do waves get reflected when they hit a harder medium (a fixed point) (Q_{8})? If the answer to Q_{8} is "Yes," is a wave that is reflected at a fixed point 180 degrees out of phase with the arriving wave (Q_{9})? Does the reflected wave at the right side fixed point travel to the left (Q_{10})? Does the reflected wave at the left side point travel to the right (Q_{11})? Is the cause of the wave appearing as a "standing wave" the repeated reflections at both of the fixed ends (Q_{12})? With the frequency at minimum, what are the number of antinodes and nodes (Q_{13})? With the frequency at the middle, what are the number of antinodes and nodes (Q_{14})? With the frequency at the maximum, what are the number of antinodes and nodes (Q_{15})?
5) Change the mode to "String fixed at one end." With the "Amplitude" at any position you want, set the frequency to minimum. Now, to your opinion, is there a wave moving to the right(Q_{16})? Is there a wave moving to the left (Q_{17})? Do waves get reflected when they hit a softer medium (a free end) (Q_{18})? If the answer to Q_{18} is "Yes," is the reflected wave at a free end in phase with the arriving wave (Q_{19})? Does the reflected wave at the right side free end travel to the left (Q_{20})? Does the reflected wave at the left side point travel to the right (Q_{21})? Is the cause of the wave appearing as a "standing wave" the repeated reflections at both ends (Q_{22})? With the frequency at minimum, what are the number of antinodes and nodes (Q_{23})? With the frequency at the middle, what are the number of antinodes and nodes (Q_{24})? With the frequency at the maximum, what are the number of antinodes and nodes (Q_{25})?
Table 1:
No. | Question | Answer |
1 | What is the "amplitude" of a wave? Definition: | |
2 | What are your estimates in "cm" of the max. and min. amplitudes on the transverse wave? | Min Amplitude = ..........cm. Max. Amplitude = ..........cm. |
3 | What wavelength do you measure with the frequency set at its minimum? | Wavelength = ......... cm |
4 | What wavelength do you measure with the frequency set at its maximum? | Wavelength = ......... cm |
5 | Why doesn't a wave on an infinitely long string return? | Ans.: |
6 | With a string fixed at both ends and put into oscillation, is there a wave moving to the right? why? | Ans.: |
7 | With a string fixed at both ends and put into oscillation, is there a wave moving to the left? why? | Ans.: |
8 | Do waves get reflected when they hit a harder medium (a fixed point)? | Ans.: |
9 | If the answer to Q_{8} is "Yes," is the reflected wave at a fixed point 180 degrees out of phase with the arriving wave? | Ans.: |
10 | Does the reflected wave at the right side fixed point travel to the left ? | Ans.: |
11 | Does the reflected wave at the left side point travel to the right ? | Ans.: |
12 | Is the cause of the wave appearing as a "standing wave" the repeated reflections at the fixed ends? | Ans.: |
13 | With the frequency at minimum, what are the number of antinodes and nodes? | Ans.: and |
14 | With the frequency at the middle, what are the number of antinodes and nodes? | Ans.: and |
15 | With the frequency at the maximum, what are the number of antinodes and nodes ? | Ans.: and |
16 | Now, to your opinion, is there a wave moving to the right? | Ans.: |
17 | Is there a wave moving to the left ? | Ans.: |
18 | Do waves get reflected when they hit a softer medium (a free end)? | Ans.: |
19 | If the answer to Q_{18} is "Yes," is the reflected wave at a free end in phase with the arriving wave? | Ans.: |
20 | Does the reflected wave at the right side (free end) travel to the left? | Ans.: |
21 | Does the reflected wave at the left side (fixed end) travel to the right? | Ans.: |
22 | Is the cause of the wave appearing as a "standing wave" the repeated reflections at both ends ? | Ans.: |
23 | With the frequency at the middle, what are the number of antinodes and nodes? | Ans.: and |
24 | With the frequency at the middle, what are the number of antinodes and nodes ? | Ans.: and |
25 |
With the frequency at the maximum, what are the number of antinodes and nodes? |
Ans.: and |
Data:
N/A
Calculations:
N/A
Comparison of the Results:
N/A
Conclusion: To be explained by students
Discussion: To be explained by students