V115.  Video Demonstration: Waves on Series Strings

First watch the video, Waves on a String: Streamed / RealPlayer / Flash

About the video:  There's no narration so we'll describe it here. Also refer to the figure below. A length of about a meter of a thin, elastic string was tied to about the same length of a thick, elastic string. The other end of the thick string was tied to a door knob to fix that end in place. The other end of the thin string was tied to a jigsaw (blade removed). The string was stretched horizontally, and the saw was turned on to put the string into vertical oscillation. The tension was adjusted to produce a wave pattern similar to the one below. The waves produced are called standing waves. While we won't study standing waves for a few days, you can still apply what you know about waves to solve the problems below. What you've learned so far are how to determine wave characteristics such as frequency, amplitude, and speed and also how to relate the wave speed to the tension and linear density of a string.

After watching the video, open the photo on this page and print it in landscape orientation. You'll need to take measurements from it as part of your solution. (Or perhaps you could just hold a ruler close to the screen to make your measurements.)

Enter your answers to the following in the corresponding WebAssign assessment.

1. How does the frequency of waves in the thick string compare to that in the thin string? It may help to view this animation where the motion is slowed down. Follow the motion of the red X's. How do their frequencies compare? If this doesn't convince you, consider the motion of the knot where the strings are tied together. At this point, both strings have the same motion.

2. How does the tension in the thick string compare to that in the thin string? Here it may be helpful to consider this situation. Suppose there's a heavy box on a table. You tie a thin string to the box and pull on it horizontally. It takes force T to make the box budge. This is the tension in the string at the instant just before the box moves. Now suppose you repeat the process after first replacing the thin string with a thick string. Does it take any more or less force to make the box budge? Finally, tie the thin string to the end of the thick string in a series arrangement and pull. Does it take any more or less force to make the box budge?

3. Determine a formula for the ratio of the wave speed in the thin string to that in the thick one. Express your formula in terms of the symbols lambda_n and lambda_k for the wavelengths of the thin and thick strings respectively.

4. Now take measurements from the video and calculate to two significant figures the ratio of the wave speed in the thin string to that in the thick.

5. Write the formula for calculating the speed of a wave in a string in terms of the tension in the string and the linear density.

6. Determine a formula for the ratio of the linear density of the thin string to that of the thick one.

7. Use your formula from the previous step to calculate the ratio of the linear densities.

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