Experiment 11
Mechanical Waves
Objective:
To visually observe the mechanical waves behavior
Equipment:
A computer with Internet connection, a calculator (The built-in calculator of the computer may be used), a few sheets of paper, and a pencil
Theory:
As an example, sound is a mechanical and longitudinal wave that travels at a speed of V = 331m/s at STP. A mechanical wave requires matter for propagation. It can not propagate in vacuum. A longitudinal wave oscillates parallel to its propagation direction. A transverse wave oscillates perpendicular to its propagation direction. At the frequency range that we mostly speak or sing (200Hz - 2000 Hz), the wavelength λ of a sound wave is in the 150cm - 15cm range. This may be verified by using the wave speed formula:
v = f λ
At this point, it is suitable to repeat the definitions of wavelength and frequency.
Wavelength: Wavelength, λ , is defined as the distance from one peak to the next one 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. Wavelength may also be defined as the distance a wave travels in each cycle.
Frequency: Frequency f is the number of waves (λ's) generated per second.
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 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 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 end travel to the left (Q_{20})? Does the reflected wave at the left end 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