Problem

A flexible stick can oscillate in a standing-wave…

01:49

Problem 73 Hard Difficulty

$\bullet$ A police siren of frequency $f_{\text { siren }}$ is attached to a vibrating
platform. The platform and siren oscillate up and down in simple harmonic motion with amplitude $A_{\mathrm{p}}$ and frequency $f_{\mathrm{P}}$ (a) Find the maximum and minimum sound frequencies that you would hear at a position directly above the siren. (b) At what point in the
motion of the platform is the maximum frequency heard? The minimum frequency? Explain.

Answer

a) $f_{L, \max }=f_{\text { siren }}\left(\frac{v}{v-(2 \pi f A)}\right) \quad, \quad f_{L, \min }=f_{\text { siren }}\left(\frac{v}{v+(2 \pi f A)}\right)$
b) The maximum frequency is detected when the platform is passing through the equilibrium position and moving up, while the minimum frequency is detected when the platform is passing through the equilibrium position and moving down.

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Physics 101 Mechanics

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Video Transcript

we are told that a police siren of frequency F siren is attached to a vibrating platform, the platform and siren Ossa late up and down in simple harmonic motion with amplitude a sepia and frequency f soapy. I want to find the max for the minimum sound frequencies that you would hear at a position directly above the siren. So we have the siren sitting on some platform that's oscillating back and forth in a simple harmonic motion. And we have, ah person appear listening to that. Um and we want to know what point is the frequency a maximum at what point is? And so we can figure out what the all right are. So are simple. Harmonic motion will just say it's a Sinus oId It doesn't really matter if it designer co sign. And then we can say that the velocity of this platform is member. With that change, our linear frequents to frequency to our circular frequency. So we need a factor of two pi. So taking the time to rebel, we get to pie Kansi amplitude frequency that it's oscillating times co sign this value here. And so we know that the max, the maximum velocity is gonna be when this thing is one. So the matter will be coefficient out here. The minimum obviously would be thing. It's minus one. And so the maximum frequency that we were here is when worst stationery. So the source is moving and so the maximum frequency will be when the source the X is positive from listener to source and then we're gonna have the philosophy is so we have be divided by the minus two pi a p f p times frequency of the source. And this will be heard when Why he is zero and the velocity is positive. So when it's going through its equilibrium position So when t because equals zero, this is a minute. Hey, when it's two pi, it's amount and then when sign of two pi zero, So why would be zero? And then in our other case, you have the platform moving away from us. So we have speed the frequency that would minimum frequency will be, um, the be the sound V plus plus two pi, a times frequency of the platform times the frequency of a siren and that will be heard when again when it's passing through. But now, when it's going down

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