# Doppler Effect Problem

1. Mar 24, 2007

### lzh

Assume: Take the speed of sound in air to be 343 m/s.
A bat, moving at 5.9 m/s, is chasing a flying insect.
The bat emits a 46 kHz chirp and receives back an echo at 46.26 kHz.
At what speed is the bat gaining on its prey? Answer in units of m/s.
I tried this:
f=initial frequency
fo=observed frequency
x= velocity of insect
fo/f=(343+Vbat)/(343+x)
but it doesn't seem to work:
46260/46000=(343+5.9)/(343+x)
1.0056=348.9/(343+x)
343+x=346.94
x=3.939
then i take the velocity of the bat:
5.9-3.939=1.96
this answer isn't right though, but I dont see why.

Last edited: Mar 24, 2007
2. Mar 24, 2007

### denverdoc

Is that the right equation to be using?

I'm getting a little confused myself, but since its an echo, I'm thinking there are two doppler shifts, one outgoing and one on the return leg, simply due do the bats speed, and then a third shift which is due to the insects motion. How did you arrive at the eqns you used?

3. Mar 24, 2007

### lzh

well technically the bat is the source, but because the chirp bounds off the insect and returns to the bat, I considered the insect to be the "source" in my equation:
f(observed)=f(init){(v+v[observer])/(v-v[source])}
v is just the speed of the sound, which is just 343. And I just plugged in all my values and solved for v[source].

4. Mar 24, 2007

### denverdoc

Good idea, and since the bat hears a blue shifted frequency, seems like you chose the right eqn, i get Vs=3.64, so the bat is making ground but at 5.9-3.64 m/s

5. Mar 25, 2007

### saplingg

Prettysure denver is right and there are 2 doppler shifts (one raising the frequency and one lowering it)

Try to draw it out on paper. Bat moving to the right shifts the frequency up. however the insect moving away shifts the frequency down.

6. Mar 25, 2007

### Staff: Mentor

There are two doppler shifts, but in both shifts the source and observer are approaching each other (relatively speaking, since the bat is gaining ground on the insect).

7. Mar 25, 2007

### lzh

how would you be able to consider two doppler shifts with one equation? We have always done single doppler shifts, and so this is pretty confusing. and denverdoc, did u get that answer with just my eqn? Or did you do some more to consider the two doppler shifts? Because i checked that answer and its not right.

8. Mar 25, 2007

### denverdoc

No I thought you had a great approach to the problem interchanging Vs and Vo from the physical situation, and just used the eqn you posted. Not sure why the answers disagree, I did'nt double check, however.

9. Mar 25, 2007

### Sourabh N

using 2 doppler shifts i got ans as 5.9 - 4.93. m i right?

10. Mar 25, 2007

### lzh

how did u get to 4.93? can u show me ur eqn?

11. Mar 25, 2007

### Sourabh N

f/fo=(343-x)(343+5.9)/(343+x)(343-5.9)
first consider bat as source & insect as observer
then exchang roles

12. Mar 25, 2007

### lzh

thats quite interesting, and makes sense. But i really can't "afford" to check the answers again(since every time i enter an answer it deducts points from my webhomework), do you guys think the way this eqn is structured is right?

13. Mar 25, 2007

### denverdoc

this was the most analogous link I could find: http://www.rwc.uc.edu/koehler/biophys/9c2.html [Broken]

From a quick glance i believe that the above looks good. Damn glad there are not relativistic issues involved as well!!

Last edited by a moderator: May 2, 2017
14. Mar 25, 2007

### Sourabh N

r u conviced with that "Izh" ?

15. Mar 25, 2007

### lzh

i think so and i will try it
but is it f/fo?

Last edited: Mar 25, 2007
16. Mar 25, 2007

### denverdoc

let us know,lzh, if that was right. Good problem.

17. Mar 25, 2007

### lzh

i got -4.177 as x, perhaps one of the signs is flipped in the eqn?

18. Mar 25, 2007

### lzh

it didn't seem to work...

19. Mar 25, 2007

### denverdoc

I got 4.93 as well.

20. Mar 25, 2007

### lzh

that didn't work...hmm i wonder what is wrong