SM_chapter16 - 16 Wave Motion CHAPTER OUTLINE 16.1 16.2...

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16 Wave Motion CHAPTER OUTLINE 16.1 Propagation of a Disturbance 16.2 The Traveling Wave Model 16.3 The Speed of Waves on Strings 16.5 Rate of Energy Transfer by Sinusoidal Waves on Strings 16.6 The Linear Wave Equation ANSWERS TO QUESTIONS Q16.1 As the pulse moves down the string, the particles of the string itself move side to side. Since the medium—here, the string—moves perpendicular to the direction of wave propagation, the wave is transverse by deF nition. *Q16.2 ±rom v = T μ , we must increase the tension by a factor of 4 to make v double. Answer (b). *Q16.3 (i) Look at the coefF cients of the sine and cosine functions: 2, 4, 6, 8, 8, 7. The ranking is d = e > f > c > b > a. (ii) Look at the coefF cients of x . Each is the wave number, 2 π / λ , so the smallest k goes with the largest wavelength. The ranking is d > a = b = c > e > f. (iii) Look at the coefF cients of t . The absolute value of each is the angular frequency ω = 2 f . The ranking is f > e > a = b = c = d. (iv) Period is the reciprocal of frequency, so the ranking is the reverse of that in part iii: d = c = b = a > e > f. (v) ±rom v = f λ = / k , we compute the absolute value of the ratio of the coefF cient of t to the coefF cient of x in each case. ±rom a to f respectively the numerical speeds are 5, 5, 5, 7.5, 5, 4. The ranking is d > a = b = c = e > f. Q16.4 To use a slinky to create a longitudinal wave, pull a few coils back and release. ±or a transverse wave, jostle the end coil side to side. *Q16.5 Answer (b). Wave speed is inversely proportional to the square root of linear density. Q16.6 Yes, among other things it depends on. The particle speed is described by v y ,max v == = ωπ Af A A 2 2 . Here v is the speed of the wave. Q16.7 Each element of the rope must support the weight of the rope below it. The tension increases with height. (It increases linearly, if the rope does not stretch.) Then the wave speed v = T increases with height. *Q16.8 (i) Answer (a). Higher tension makes wave speed higher. (ii) Answer (b). Greater linear density makes the wave move more slowly. 383
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384 Chapter 16 *Q16.9 (i) Answer a. As the wave passes from the massive string to the less massive string, the wave speed will increase according to v = T μ . (ii) Answer c. The frequency will remain unchanged. However often crests come up to the boundary they leave the boundary. (iii) Answer a. Since v = f λ , the wavelength must increase. Q16.10 Since the frequency is 3 cycles per second, the period is 1 3 second = 333 ms. Q16.11 Let Δ tt t sp =− represent the difference in arrival times of the two waves at a station at distance dt t ss pp == vv from the hypocenter. Then Δ 11 1 . Knowing the distance from the F rst station places the hypocenter on a sphere around it. A measurement from a second sta- tion limits it to another sphere, which intersects with the F rst in a circle. Data from a third non-collinear station will generally limit the possibilities to a point.
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This note was uploaded on 01/28/2011 for the course PHYS 011 taught by Professor Nianlin during the Fall '08 term at HKUST.

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SM_chapter16 - 16 Wave Motion CHAPTER OUTLINE 16.1 16.2...

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