Explanation Given data: Consider the microphone (at the platform) as observer, and the loudspeaker as the source. The frequency emitted by the loudspeaker (source frequency) ( f s ) is 1.000 × 10 4 Hz . Speed of the sound ( v ) is 343 m s . The frequency observed by the microphone at a time of 1.5 s following the release of the platform ( f o, 1 .5 s ) is 9939 Hz. The frequency observed by the microphone at a time of 3.5 s following the release of the platform ( f o, 3. 5 s ) is 9857 Hz. Formula used: Refer to the equation (2.4) in the textbook, and modify the expression for acceleration of the platform as follows. a = v o, 3. 5 s − v o, 1. 5 s t o, 3. 5 s − t o, 1. 5 s (1) Here, v o, 3. 5 s is the velocity of the platform at the time of 3.5 s, v o, 1. 5 s is the velocity of the platform at the time of 1.5 s, t o, 3. 5 s is the time at the time of 3.5 s, which is 3.5 s, and t o, 1. 5 s is the time at the time of 1.5 s, which is 1.5 s. From the given data, the observer (platform) moves away from the source (loudspeaker). As the observer moves away from the source, refer to the equation (16.14) in the textbook, and modify the expression for observed frequency by the microphone at a time of 1.5 s following the release of the platform as follows. f o, 1 .5 s = f s ( 1 − v o, 1 .5 s v ) (2) Here, f s is the source frequency, and v is the speed of the sound. As the observer moves away from the source, refer to the equation (16.14) in the textbook, and modify the expression for observed frequency by the microphone at a time of 3.5 s following the release of the platform as follows. f o, 3. 5 s = f s ( 1 − v o, 3. 5 s v ) (3) Calculation of velocity of the platform at the time of 1.5 s ( v o, 1. 5 s ) : Rewrite the expression in equation (2) to find the velocity of the platform at the time of 1.5 s as follows. f o, 1 .5 s f s = 1 − v o, 1 .5 s v v o, 1 .5 s v = 1 − f o, 1 .5 s f s v o, 1 .5 s = v ( 1 − f o, 1 .5 s f s ) Substitute 343 m s for v , 9939 Hz for f o, 1 .5 s , and 1.000 × 10 4 Hz for f s , v o, 1

10th Edition

ISBN: 9781119081739

Author: CUTNELL

Publisher: WILEY

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Chapter 16, Problem 84P

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To find: The acceleration of the platform.

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Chapter 16, Problem 83P

Chapter 16, Problem 85P

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