Problem A wireless transmitting microphone ismounted on a small platform, which

Question

Problem A wireless transmitting microphone ismounted on a small platform, which can roll down an incline, awayfrom a speaker that is mounted at the top of the incline. Thespeaker broadcasts a fixed-frequency tone.

(a1) The speaker broadcasts a tone that has afrequency of 1.000 × 104 Hz, and thespeed of sound is 343 m/s. At a time of 1.5s following the release of the platform, the microphonedetects a frequency of 9733 Hz. At a time of 3.5s following the release of the platform, the microphonedetects a frequency of 9378 Hz. What is theacceleration a (assumed constant) of the platform?

WILL RATE LIFESAVER!!!!

THANKS!

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)(1-9733/10000)              = 9.16 m/s      for t = 3.5s     vmike2 = (343)(1-9378/10000)              =  21.33 m/s the acceleration of the platform is     a = 21.33 m/s - 9.16 m/s /3.5s-1.5s        = 6.085m/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)(1-9733/10000)              = 9.16 m/s      for t = 3.5s     vmike2 = (343)(1-9378/10000)              =  21.33 m/s the acceleration of the platform is     a = 21.33 m/s - 9.16 m/s /3.5s-1.5s        = 6.085m/s2              =  21.33 m/s the acceleration of the platform is     a = 21.33 m/s - 9.16 m/s /3.5s-1.5s        = 6.085m/s2

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