Doppler effect with frequency ratio

[wolfsrain159]

Homework Statement

An avant-garde composer wants to use the Doppler effect in his new opera. As the soprano sings, he wants a large bat to fly toward her from the back of the stage. The bat will be outfitted with a microphone to pick up the singer's voice and a loudspeaker to rebroadcast the sound toward the audience. The composer wants the sound the audience hears from the bat to be, in musical terms, one half-step higher in frequency than the note they are hearing from the singer. Two notes a half-step apart have a frequency ratio of 2^(1/12) = 1.059.

Homework Equations

The Attempt at a Solution

I used f' = (c/c + Vs)f and f' = (c/c-Vs) because I was unsure which one to use. I plugged in c = 340 m/s and just divided f'/f and had that equal the frequency ratio. I kept getting answers like 19 m/s and 20 m/s but that isn't right

 

[haruspex]

I used f' = (c/c + Vs)f and f' = (c/c=Vs)

You mean f'= c/(c-Vs).
One way to remember which to use is to consider the boundary case where the source is moving at speed c. The sound waves move with the source, piling up as an unlimited number of wavefronts at its leading edge. So when the source arrives at the receiver, all waves are heard in an instant, i.e. an infinite frequency. So it must be the c/(c-...) form.
I agree with 19m/s, or nearly. Do you know what the 'book' answer is? Could it be a matter of significant digits?

Edit: ouch - I got myself confused. I explained how to figure out which to use, then used the wrong one.
The correct conclusion is that it should be the "+" form. (Thanks, Doc Al.). But your equation for that case is inverted.

 

[wolfsrain159]

You mean f'= c/(c-Vs).
One way to remember which to use is to consider the boundary case where the source is moving at speed c. The sound waves move with the source, piling up as an unlimited number of wavefronts at its leading edge. So when the source arrives at the receiver, all waves are heard in an instant, i.e. an infinite frequency. So it must be the c/(c-...) form.
I agree with 19m/s, or nearly. Do you know what the 'book' answer is? Could it be a matter of significant digits?

Thank you for correcting that, I made a typo. This problem is from my online homework and the only instructions it says is to enter the answer with the proper units, which for velocity is m/s. Other then that I have no idea what I'm doing wrong. Using the second form c/(c-...) I got 19.098 m/s but I had already entered 19 m/s and 19.1 m/s and it said both were incorrect.

 

[Doc Al]

(1) What frequency does the bat observe and retransmit?
(2) What frequency does the audience observe emitted by the bat?

 

[haruspex]

Using the second form c/(c-...) I

Please see my edit at post #2.

 

[wolfsrain159]

Please see my edit at post #2.

Using the other form c/(c+...) I got -19.1, which I'm assuming is negative for the direction. However, usually the online program will let you know if your sign is incorrect and it didn't say anything about it. I just don't want to use all my tries if it is still "incorrect"

 

[haruspex]

Using the other form c/(c+...) I got -19.1, which I'm assuming is negative for the direction. However, usually the online program will let you know if your sign is incorrect and it didn't say anything about it. I just don't want to use all my tries if it is still "incorrect"

Did you read the last sentence of my updated post #2? It was a second edit, so you might have missed it.

 

[wolfsrain159]

Did you read the last sentence of my updated post #2? It was a second edit, so you might have missed it.

so would I use (c+Vs)/c = f' ?

 

[haruspex]

so would I use (c+Vs)/c = f' ?

Yes.

 

[wolfsrain159]

Yes.

I got 20.247 using that equation and 20 m/s was marked incorrect. Would I inverse f' as well? Like use 1/1.0595 instead?

 

[haruspex]

I got 20.247 using that equation and 20 m/s was marked incorrect. Would I inverse f' as well? Like use 1/1.0595 instead?

It gives me 20.217. But that only arranges that the frequency picked up by the bat is a half step higher. Note Doc Al's second question.