Calculating Bat Flight Speed Using the Doppler Effect

In summary: The bat emits a frequency of 25.0 kHz. The bat hears its own sound plus the sound reflected by the wall. The speed of sound is 344 m/s. To hear a beat frequency of 220 Hz, the bat should fly at a speed of v_b = 280.296 m/s.
  • #1
wimma
38
0

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
 
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  • #2
Your answer for

[tex]f_{received by bat} = \frac{v_{sound} + v_{bat}}{v_{sound} - v_{bat}} f_{emitted}[/tex]

seems to be right.

So your [tex]f_{beat}[/tex] is alright too.

Getting [tex]v_{bat}[/tex] is just a matter of algebra and substituting the right values.

The answer should have order of magnitude [tex]a * 10^0[/tex].
 
Last edited:
  • #3
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)
 
  • #4
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
 
  • #5
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
 
  • #6
Could you show yours?
 

What is the Doppler effect bat problem?

The Doppler effect bat problem is a theoretical scenario used to demonstrate the concept of the Doppler effect, which describes the apparent change in frequency of a wave due to the relative motion between the source of the wave and the observer.

How does the Doppler effect apply to the bat problem?

In the bat problem, a bat flying towards an observer emits ultrasonic waves. As the bat moves closer, the waves are compressed, resulting in a higher frequency. As the bat flies away, the waves are stretched, resulting in a lower frequency. This change in frequency is perceived as a change in pitch by the observer, allowing them to locate the bat.

Why is the Doppler effect important in understanding bat behavior?

The Doppler effect is crucial in understanding bat behavior because it allows bats to accurately navigate and locate prey in the dark, using echolocation. By emitting high-frequency sound waves and interpreting the returning echoes, bats can determine the location, size, and direction of their prey.

How does the speed of the bat affect the Doppler effect?

The speed of the bat directly affects the intensity of the Doppler effect. The faster the bat flies, the greater the change in frequency between the emitted and received waves. This means that a faster-moving bat will experience a more significant change in pitch, making it easier for the observer to detect.

What are some real-world applications of the Doppler effect bat problem?

The Doppler effect bat problem has several real-world applications, including radar technology, medical imaging, and studying the movement of stars and other celestial bodies. It has also been used to develop ultrasonic sensors for detecting and measuring the speed of moving objects.

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