A helicopter drops a paratrooper carrying a buzzer that emits a 500 Hz signal. A sound receiver on the plane monitors the signal as the paratrooper falls. If the perceived frequency becomes constant at 450 Hz, what is the terminal speed at the paratrooper ? Take the speed sound in air to be 343 m/s and assume the paratrooper always remains below the helicopter.

The percentage change in frequency heard by the helicopter is equal to the ratio of the paratrooper's speed to the speed of sound. Can you complete this now?

How to do it?

Let:


v_s = speed\ of\ sound\\
v_p\ =\ speed\ of\ paratrooper\\
f_e\ =\ frequency\ of\ signal\ emitted\ by\ the\ beeper\\
f_r\ =\ frequency\ of\ signal\ received\ at\ the\ helicopter


Then:


\Delta f = f_e-f_r \\
\frac {\Delta f} {f_e} = \frac {v_p} {v_s}


You have all the data you need to rearrange and solve for v_p.

Thanks