Frequency Heard By Person-I got the first part but am confused how to calculate frequency behind car.

Question

An opera singer in a convertible sings a note at 700 Hz while cruising down the highway at 86 km/h. The speed of sound in the air is 343 m/s.

frequency heard by a person standing beside the road in front of the car=750 Hz

What is the frequency heard by a person standing beside the road behind the car?

Answer 1

O = observer

S = source

Dopler effect for sound: fo = fs (v + vo) / (v + vs)

vo = 0 (the observer is not moving with respect to air)

v = 343 m/s (speed of sound with respect to air)

vs = 86 km/h (speed of the source with respect to air, convert to m/s)

For an observer in front of the car, the observed frequency fo is higher (higher pitch), so take vs = - 86 km/h in the formula. That gives you a smaller denominator in the formula and a larger result for fo.

For an observer behind the car, the observed frequency fo is lower (lower pitch), so take vs = + 86 km/h. That gives you a larger denominator in the formula and a smaller result for fo.

I hope that helps.