Hand In 6 Solutions(07)

Hand In 6 Solutions(07) - Solutions for Hand-In Set#6 PHYS...

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Solutions for Hand-In Set #6 PHYS 212 – Spring 2007 A32 — Traveling Waves on a Magic Spring For the longitudinal wave, I found that the pulse did about 5 full round trips in about 4.4 seconds. (It was a bit difficult to be precise here — I used a stop watch, but deciding exactly when the pulse returned was not easy; I didn’t measure the length with any precision either.) So, v long = (5 round trips) × (4 m/trip) 4 . 35 sec = 4 . 6 m/s . For the transverse wave, I found that the pulse did about 5 round trips in 4.0 seconds, so v tran = 5 round trips × (4 m/trip) 4 . 0 sec = 5 . 0 m/s . Comparing this to what I got for A33, in that problem, I got about 5 m/s for the propagation speeds of transverse waves, so the result is quite consistent, considering that the uncertainties in my measurements. A33 — Standing Waves on a Magic Spring I made qualitative estimates holding the slinky in my hands. It was pretty to easy to generate the fundamen- tal, first, and second harmonics. The frequency of the first harmonic was approximately twice that of the fun- damental, and the frequency of the second harmonic was approximately three times that of the fundamental. It was trickier to generate higher harmonics, and it was even harder to make good estimates of the frequencies, but they were definitely at higher frequencies. To make some quantitative estimates for comparison with the result of problem A32 I stretched my spring to the same length as the length I used in A32 (about 2 m). Here are my results: mode # osc. Time (s) T (s) f (Hz) λ (m) v = λf n = 1 10 8.3 0.83 1.20 4 4.8 n = 2 20 8.12 0.41 2.5 2 5.0 n = 3 40 10.5 0.26 3.8 1.33 5.1 I had difficulty making good measurements for n = 4 and higher, but my results for n = 1 n = 3 are very consistent with the speed of transverse waves determined in A32.
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