Question

This A siren mounted on the roof of a firehouse emitssound at a frequency of 900Hz. A steady wind is blowing witha speed of 15.0 m/s. Taking the speed of sound in calm air tobe 343 m/s, find the wavelength of the sound (a) upwind of thesiren and (b) downwind of the siren. Firefighters areapproaching the siren from various directions at 15.0 m/s. Whatfrequency does a firefighter hear (c) if she is approaching from anupwind position so that she is moving in the direction in which thewind is blowing and (d) if she is approaching from a downwindposition and moving against the wind? In parts c and d, how are the velocities of the observer and source calculated?

Answer 1

f=900Hz, v_s = 343 m/s, v_w = 15m/s

a)

v_upwind = v_s + v_w = 343m/s + 15 m/s = 358 m/s

λ_upwind = (v_upwind)/f = 358/900 = 0.40m

b)

v_downwind = v_s - v_w = 343m/s - 15 m/s = 328 m/s

λ_downwind = (v_downwind)/f = 328/900 = 0.36m

c)

When she is approaching from an upwind position, she is moving in the direction in which the wind is blowing.

But directions of siren and wind are opposite.

Using Doppler’s law,

f' = f(v_downwind + v_observer )/ v_downwind

f' = 900(328 + 15)/328

f' = 941.16 Hz

d)

When she is approaching from an downwind position, she is moving in the opposite direction in which the wind is blowing.

But directions of siren and wind are same.

Using Doppler’s law,

f' = f(v_upwind + v_observer )/ v_upwind

f' = 900(358 + 15)/358

f' = 937.71 Hz