You are in a fire truck heading directly toward a tunnel in

You are in a fire truck heading directly toward a tunnel in a mountainside at 17m/s. you hear the truck\'s 90Hz siren as well as its reflection from the mountainside. What beat frequency do you hear?

Solution

Take the speed of sound to be 343m/s.

Direct frequency perceived by observer = ((343 + 17)/343) x 90Hz = 94.460Hz.

Change in frequency = (94.460 - 90) = 4.460Hz.

90 - (4.460 x 2) = 81.08 Hz. indirect frequency heard by observer.
Beat frequency = (94.460 - 81.08) = 13.38Hz.