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Doppler Shift

  • #1
JJBladester
Gold Member
286
2

Homework Statement



Imagine that the source is to the right of the listener, so that the positive reference direction (from the listener to the source) is in the [itex]+\hat{x}[/itex] direction. If the listener is stationary, what value does [itex]f_L[/itex] approach as the source's speed approaches the speed of sound moving to the right?


Homework Equations



[tex]f_L=f_s\left ( \frac{v+v_L}{v+v_s} \right )[/tex]

Where [itex]v[/itex] is the speed of the sound in the medium,
[itex]v_L[/itex] is the velocity of the listener, and
[itex]v_s[/itex] is the velocity of the source.

The Attempt at a Solution



I'm assuming that the speed of sound, being so large can be seen as [itex]v_s[/itex] approaching infinity.

I think the way to solve this problem is to take the following limit:

[tex]\lim_{v_s \to \infty }f_s\left ( \frac{v+v_L}{v+v_s} \right )[/tex]

The answer given is that [itex]f_L[/itex] approaches [itex]\frac{1}{2}f_s[/itex].

I'm not sure how to evaluate the limit to get the answer.
 

Answers and Replies

  • #2
JJBladester
Gold Member
286
2
Got it... [itex]v_s \to v[/itex] so the limit is just a simple substitution and the answer makes sense. I misunderstood what "the speed of sound" meant.
 

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