A wireless transmitting microphone is mounted on a small platform,which can roll

Question

A wireless transmitting microphone is mounted on a small platform,which can roll down an incline, away from a speaker that is mountedat the top of the incline. The speaker broadcasts a fixed-frequencytone.

The speaker broadcasts a tone that has a frequency of 1.000 ×104 Hz, and the speed of sound is 343 m/s. At a time of 1.5 sfollowing the release of the platform, the microphone detects afrequency of 9952 Hz. At a time of 3.5 s following the release ofthe platform, the microphone detects a frequency of 9888 Hz. Whatis the acceleration a (assumed constant) of the platform?



Thanks for your help!

Explanation / Answer

The change in velocity is related to the acceleration of theplatform according to    a =vmike2-vmike1/t-t0 The frequency detected by the microphone at the instant theplatform is released from rest is fo =fs{1-(vmike/v)}   or    vmike =v(1-f0/fs)    for t= 1.5s      vmike1 = (343)(1-9952/10000)              = 1.64 m/s      for t = 3.5s     vmike2 = (343)(1-9888/10000)              =  3.84 m/s the acceleration of the platform is     a = 3.84 m/s - 1.64 m/s /3.5s-1.5s        = 1.1m/s2 The frequency detected by the microphone at the instant theplatform is released from rest is fo =fs{1-(vmike/v)}   or    vmike =v(1-f0/fs)    for t= 1.5s      vmike1 = (343)(1-9952/10000)              = 1.64 m/s      for t = 3.5s     vmike2 = (343)(1-9888/10000)              =  3.84 m/s the acceleration of the platform is     a = 3.84 m/s - 1.64 m/s /3.5s-1.5s        = 1.1m/s2              =  3.84 m/s the acceleration of the platform is     a = 3.84 m/s - 1.64 m/s /3.5s-1.5s        = 1.1m/s2

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