Doppler effect (source and detector moving together)

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A source emitting sound at 860 Hz moves toward a stationary wall at 20.0 m/s, with the speed of sound being 343 m/s. To determine the frequency heard by an observer riding with the source, the problem requires calculating the frequency received at the wall first, treating the reflected sound as a new source. The initial calculation incorrectly assumed the frequency remained constant, but the correct approach involves two steps: first finding the frequency at the wall and then the frequency heard by the observer. Ultimately, the frequency heard by the observer is calculated to be 976 Hz. Understanding the Doppler effect in this context necessitates recognizing the interaction between the source and the reflecting wall.
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Homework Statement



A source emits sound with a frequency of 860 Hz. It is moving at 20.0 m/s toward a stationary reflecting wall. If the speed of sound is 343 m/s, what frequency does an observer riding with the source hear?

  • A

    860 Hz


  • B

    913 Hz


  • C

    910 Hz


  • D

    765 Hz

  • E

    967 Hz

Homework Equations


CodeCogsEqn-4.gif

WHERE FL and vL are the frequency and velocity of sound heard by the personL
fs and vs are the frequency and velocity of sound emmited by the source

The Attempt at a Solution

:[/B]
v=343 m/sec
vs=20 m/sec
vL=-vs=-20 m/sec since if it is moving away from the source
fs=860Hz
then using the aboove equation
CodeCogsEqn-4.gif

FL=860Hz=Fs
but it is incorrect? Why?
 
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You need to do this in two steps. Step one: What is the frequency received at the wall? (Then treat the reflected sound from the wall as the new source.)
 
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Doc Al said:
You need to do this in two steps. Step one: What is the frequency received at the wall? (Then treat the reflected sound from the wall as the new source.)
Ah then vs=vL since both are coming toward each other.
then fL=976 Hz which is correct :) thanks
 
Doc Al said:
You need to do this in two steps. Step one: What is the frequency received at the wall? (Then treat the reflected sound from the wall as the new source.)
Suppose we don't have a wall, then how are we supposed to find that frequency received by the person?
 
Any Help said:
Suppose we don't have a wall, then how are we supposed to find that frequency received by the person?
Not sure what you mean. What is he hearing? (There needs to be a source of sound.)
 
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The answer is (B) but I don't really understand why. Based on formula of Young Modulus: $$x=\frac{FL}{AE}$$ The second wire made of the same material so it means they have same Young Modulus. Larger extension means larger value of ##x## so to get larger value of ##x## we can increase ##F## and ##L## and decrease ##A## I am not sure whether there is change in ##F## for first and second wire so I will just assume ##F## does not change. It leaves (B) and (C) as possible options so why is (C)...

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