Time taken for sound to travel between two moving observers

  • #1
Saptarshi Sarkar
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Homework Statement:
A source S of frequency ##f_0## and an observer O, moving with speeds ##v_1## and ##v_2## respectively, are moving away from each other. When they are separated by distance a (t=0), a sound pulse is emitted by the source. Suppose velocity of sound to be ##v_s## and calculate the time ##t_1## that it takes for the pulse to be received by O.
Relevant Equations:
Total distance the pulse needs to travel:
##D = a + v_1t_1##

Speed of sound pulse = ##v_s - v_2##

So,
##t_1 = \frac {a + v_1t_1} {v_s - v_2}##
But the solution should be

##t_1 = \frac a {v_s - v_2}##

I assumed the following -

1. I did not consider the frequency as the Doppler shift in frequency was not asked.

2. I did not add the distance the source moved in time ##t_1## to the total distance traveled by the wave as the pulse was emitted at t=0.

Is any of my assumptions wrong?
 

Answers and Replies

  • #2
haruspex
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Please explain your reasoning for your expression for D.
You could sketch the motions of source, observer and pulse on a distance-time graph.
 
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  • #3
PeroK
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So,
##t_1 = \frac {a + v_1t_1} {v_s - v_2}##

I assumed the following -

2. I did not add the distance the source moved in time ##t_1## to the total distance traveled by the wave as the pulse was emitted at t=0.

How is that equation based on your assumption?

Are taking ##v_2## to be the speed of the source?
 
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  • #4
Saptarshi Sarkar
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Sorry, I guess I messed up the velocities. I will edit the question and add a sketch tomorrow morning.
 
  • #5
Saptarshi Sarkar
99
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Can't edit the question, so posting it here

Homework Statement::


A source S of frequency ##f_0## and an observer O, moving with speeds ##v_1## and ##v_2## respectively, are moving away from each other. When they are separated by distance a (t=0), a sound pulse is emitted by the source. Suppose velocity of sound to be ##v_s## and calculate the time ##t_1## that it takes for the pulse to be received by O.
Homework Equations::

Total distance the pulse needs to travel:
##D = a + v_2t_1##

Speed of sound pulse = ##v_s - v_1##

So,
##t_1 = \frac {a + v_2t_1} {v_s - v_1}##

But the solution should be

##t_1 = \frac a {v_s - v_2}##

I assumed the following -

1. I did not consider the frequency as the Doppler shift in frequency was not asked.

2. I did not add the distance the source moved in time ##t_1## to the total distance traveled by the wave as the pulse was emitted at t=0.

Is any of my assumptions wrong?

15775402198826710203335089938639.jpg
 
  • #6
PeroK
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The speed of sound in a medium is independent of the motion of the source.
 
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  • #7
Saptarshi Sarkar
99
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The speed of sound in a medium is independent of the motion of the source.

Thanks!
 

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