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Unformatted text preview: Walker CH 14 Solutions Chapter 14: Waves and Sound Answers to Even-Numbered Conceptual Questions 2. Waves passing through a field of grain are longitudinal wavesthe motion of each stalk of grain is in the same direction as the motion of the wave itself. 4. This wave is longitudinal, since each cat moves in the same direction as the wave. 6. The Doppler effect applies to radar waves as well as to sound waves. In particular, the ball sees a Doppler- shifted radar frequency for the waves coming from the radar gun. Then, the ball acts as a moving source for waves of this frequency, giving a second Doppler shift to the echoes that are picked up by the radar gun. This provides a one-to-one correspondence between the final observed frequency and the speed of the ball. 8. The sliding part of a trombone varies the length of the vibrating air column that produces the trombones sound. By adjusting this length, the player controls the resonant frequencies of the instrument. This, in turn, varies the frequency of sound produced by the trombone. 10. The thicker string is used to produce the low-frequency notes. This follows because the frequency of the fundamental depends directly on the speed of waves on the string. Therefore, for a given tension, a string with a greater mass per length has a smaller wave speed and hence a lower frequency. 12. You have just observed a series of beats between your wipers and the wipers of the other car. Answers to Even-Numbered Conceptual Exercises 2. Referring to / v F = (equation 14-2), we see that to double the speed, the tension F in the string must be increased by a factor of 4. 4. The thick string (string 1) has more mass per length than the thin string (string 2). Therefore, if the wave speed is the same, the tension in string 1 must be greater than the tension in string 2. 6. (a) When the string is displaced (stretched) by its greatest amount, its potential energy is a maximum, just as in the case of a spring. (b) At zero displacement, the string is like a spring at its equilibrium position. Therefore, the potential energy of the string is a minimum. 8. As the wave moves to the right, the peak that was at point A will move to point B. As a result, we have the following results: A, instantaneously at rest; B, moving upward; C, moving upward; D, instantaneously at rest; E, moving downward; F, moving downward. 10. (a) This wave travels in the negative x direction, because Bx + Ct = (constant) implies x = (constant)/ B ( C / B ) t . (b) The constant A is the amplitude of the wave. (c) The speed of this wave, as can be seen from part (a), is C / B . (d) The times when y = 0 at x = 0 are given by ( ) ( ) sin 0 sin y A Ct A Ct = + = = . The smallest positive time that satisfies A sin ( Ct ) = 0 is t = / C ....
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This note was uploaded on 03/19/2011 for the course BIOL 140 taught by Professor Dr.joshneufeld during the Spring '10 term at Waterloo.
- Spring '10