How Many Beats per Second Will the Runner Hear Due to Sound Interference?

AI Thread Summary
The discussion revolves around calculating the number of beats per second a runner will hear from a car honking a 2kHz tone, considering both the direct sound and the echo reflected from a wall. The Doppler effect is crucial in determining the frequency changes due to the runner's movement. The runner is moving at 5 m/s, and the problem requires understanding how his velocity affects the perceived frequency from both the car and its reflected image. Key points include calculating the distances from the runner to both the car and its reflection, as well as determining the effective speed of sound in relation to the runner's position. The overall goal is to find the beat frequency resulting from the interference of the two sound waves.
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Homework Statement


A car honks a 2kHz tone and is 40m from a long high wall. A man is running parallel to the wall, 10m away from it, at 5 m/s, and is presently 30m away from where the whistle is closest to the wall. How many beats/second will be heard by the runner as he will hear the direct whistle signal and the one reflected from the wall.


Homework Equations


The Attempt at a Solution



I have drawn a diagram and also knw that this problem has to do with the Doppler effect.
But i am not sure where to start.
 

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You can treat the echo as coming from another source, being the image of the car reflected in the wall. How fast is the man moving away from the car? From the image car?
 
okay so i know that the man is moving 5m/s and the frequency at the source will be
2kHz but how would i found the seed of the wave...will it just be speed of sound?
 
He's moving at 5m/s, but how fast is he moving away from the car?
 
aright the man is 42.42m away from the car and 31.62m away from the reflection...but would he not be moving away at 5m/s from both these points aswell?
if not how would u figure that out?
 
Velocity is a vector. What is the component of the man's velocity along the line from car to man?
What do you mean by "the man is 31m from the reflection? It's the distance and speed from the car's 'image' reflected in the wall that matters.
 
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