A siren mounted on the roof of a firehouse emits sound at a frequency of 900 Hz.
ID: 1536753 • Letter: A
Question
A siren mounted on the roof of a firehouse emits sound at a frequency of 900 Hz. A steady wind is blowing with a speed of 15.0 m/s. taking the speed of sound in calm air to be 343 ms, find the wavelength of the sound Upwind (the direction the wind is coming from) of the siren and downwind (the direction in which to wind is blowing) of the siren. Firefighters are approaching the siren from various directions at 15.0m/s. What frequency does a Firefighter hear if he or she is approaching from an upwind position, so that he is moving in the direction in which the wind is blowing? If he or she is approaching from an downwind position and moving against the wind?Explanation / Answer
a )
given
speed of the sound in air V = 344 m/sec
freuency of the sound is f = 900 Hz
Speed of the wind v = 15 m/sec
wavelength upwind of siren is = V - v / f
= 344 - 15 / 900
= 0.3655 m
b )
wavelength downwind of siren is = V + v / f
= 344 + 15 / 900
= 0.3988 m
c )
speed of the fire fighters v0 = 15 m/sec
the velocity of sound becomes ( 344 - 15 ) = 329 m/sec
apparent frequency f ' = ( 329 + 15 / 329 ) X 900
f ' = 941.033 Hz
d )
speed of the fire fighters v0 = 15 m/sec
the velocity of sound becomes ( 344 + 15 ) = 359 m/sec
apparent frequency f ' = ( 359 + 15 / 329 ) X 900
f ' = 937.6 Hz