Calculating Bat Flight Speed Using the Doppler Effect

[wimma]

Homework Statement

A bat flies toward a wall, emitting a steady sound with a frequency of 25.0 kHz. This bat hears its own sound plus the sound reflected by the wall.


How fast should the bat fly, v_b, to hear a beat frequency of 220 Hz?

Take the speed of sound to be 344 m/s.

Homework Equations

f_beat = f_a - f_b

The Attempt at a Solution

I let the speed of sound be v and let the emitted frequency be f_e and got an expression for the beat frequency:
f_beat = ((v+v_b)/(v-v_b)-1)f_e
Didn't get the right answer... Doing it another way I got
f_beat = (v^2/(v-v_b)^2 - 1)f_e

 

[Hao]

Your answer for

$$f_{received by bat} = \frac{v_{sound} + v_{bat}}{v_{sound} - v_{bat}} f_{emitted}$$

seems to be right.

So your $$f_{beat}$$ is alright too.

Getting $$v_{bat}$$ is just a matter of algebra and substituting the right values.

The answer should have order of magnitude $$a * 10^0$$.

 

[wimma]

MasteringPhysics still fails me on that answer
Note: I compute 280.296 m/s

Why would it be that order of magnitude? (Other than common sense to do with a bat)

 

[Hao]

What is the numerical answer they quote (if they provide one)?

There are several ways this analysis can go wrong.

1) If you do not account for the fact that the frequency is doppler shifted on reception, the numerator goes from c+v to just c.

2) If you do not account for the fact that the frequency is doppler shifted on emission, the denominator goes from c-v to just c.

I compute 1.507 m/s

 

[wimma]

Thanks for your help, though I don't understand how you got that answer...

We go f_beat = f_receive - f_transmit

and when I substitute in I get the wrong answer... your answer was correct by the way.

Could you please put in your substitution steps? Thanks

 

[diazona]

Could you show yours?