How Fast is the Ambulance Traveling in the Doppler Effect Problem?

[booj1204]

Homework Statement

You are traveling north of wayne rd at 20.0m/s, when you notice an ambulance in the distance approaching you at a high rate of speed. Using an iPhone app, you measure the siren's frequency to be 1.427 kHz. From previous experience you know that the ambulance siren emits a tone of 1.200kHz. the speed of sound in air is 343m/s.

a) How fast is the ambulance traveling south on wayne?


b) Assuming that your have stopped while the ambulance passes you, what do you measure for the frequency of the siren as the ambulance speeds away from you?

Homework Equations

a) (v0/v) = 1-(vs/v)(f0/fs)-1

b) f0=fs(1/(1+vs/v)

The Attempt at a Solution

a) (v0/v) = 1-(vs/v)(f0/fs)-1

=> (1-(20.0/343))(.1200 Hz/.1427 Hz) - 1 = .208

v0=v(0..208) = 343 m/s (0.208) = 71. 38m/s

b) f0=fs(1/(1+vs/v)

=> .1427 (1/1+20.0/343) = 0.134 Hz

I would really appreciate if someone would let me know if my solution is correct. Thanks!

 

[anathema]

I would like to clarify some points in your solution:

a) The formula you used is correct, but the value you obtained for v0 is incorrect. It should be 25.54 m/s, not 71.38 m/s. This is because you used the wrong value for v0. In this case, v0 is the speed of sound in air, which is 343 m/s. So the equation should be (343/343) = 1 - (vs/343)(1200/1427), which gives a value of 25.54 m/s for vs.

b) Your formula for b) is incorrect. The correct formula is f0=fs(343/(343+vs)), which gives a value of 1.288 kHz for the frequency of the siren as the ambulance speeds away from you.

I hope this helps clarify any misunderstandings. Keep up the good work!