What is the terminal speed of the paratrooper?

[European Sens]

Homework Statement

A helicopter drops a paratrooper carrying a siren that emits a 788 Hz audible signal. The microphone (reciever) on the plane monitors the signal from the transmitter as the paratrooper falls. Take the speed of sound in air to be 343 m/s and assume the paratroopers always remains below the helicopter. If the perceived frequency becomes constant at 412 Hz, what is the terminal speed of the paratrooper? Answer in units of m/s.

Homework Equations

Not sure... could you guys help me out.

Possibly Speed = wavelength * frequency ??

The Attempt at a Solution

Probably would need an equation first.

 

[Ed Aboud]

Try and use your knowledge of the doppler effect for this.

 

[European Sens]

I don't really know much about it.

f' = f [(v+v1)/(v-v2)]

that's the equation. could you please walk me through this problem.

 

[Ed Aboud]

Ok so the doppler effect is the apparent change in frequency of a wave due to the motion of the source or the observer.
So f' is the observed and f is the frequency of the source.

$$f' = \frac{fv}{v\pm u}$$

where v is the speed of sound and u is the speed of the source or the observer.
If the source is approaching you it is v - u and if it is moving away it is v + u.

 

[European Sens]

Okay. That was very helpful. I got the answer of 313.03.

I submitted online and it is correct.

Thanks!

 

[Ed Aboud]

No problem, happy to help.