Question
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In the figure below is shown a picture of a string at a time t1. The pieces of the string are each moving with velocities which are indicated by arrows in the picture. (The vertical displacements are small and don't show up in the picture.)

Below are shown five graphs which could give the shape of the string at the instant for which the velocities are displayed above. (Note: the vertical scale magnifies the displacement by a factor of 100.)

For each of the cases A - E choose whether the string that has that position graph and the velocity pattern at the top is moving as a: (L) left-traveling wave (R) right traveling wave (S+) a standing wave increasing in amplitude (S-) a standing wave decreasing in amplitude (N) none of the above.

1. For graph A: ---Select--- L R S+ S- N

2. For graph B: ---Select--- L R S+ S- N

3. For graph C: ---Select--- L R S+ S- N

4. For graph D: ---Select--- L R S+ S- N

5. For graph E: ---Select--- L R S+ S- N

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Step 1

To find the answers we simply look at the velocity profile and impose it on the position graphs to find the infinitesimal displacement in a small interval of time. We can see that,

1. For graph A the positions of troughs and peaks will remain stationary while the amplitude will decrease. Therefore we will have a standing wave with decreasing amplitude that is S-.

Step 2

2. For graph B a peak rises at 1/4 the wavelength and a trough will form at 3/4 the wavelength. Therefore we will have a wave travelling to the right that is R.

3. For graph C we will have a peak forming at 1/4 the wavelength and a trough forming at 3/4th the wavelength. Therefore we will have a wave travelling to the left. That is L.

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