Answer:
70 Hz
Explanation:
The Doppler equation describes how sound frequency depends on relative velocities:
fr = fs (c + vr)/(c + vs),
where fr is the frequency heard by the receiver,
fs is the frequency emitted at the source,
c is the speed of sound,
vr is the velocity of the receiver,
and vs is the velocity of the source.
Note: vr is positive if the receiver is moving towards the source, negative if away. Â
Conversely, vs is positive if the receiver is moving away from the source, and negative if towards.
When the car is approaching you:
fr = 76 Hz
vr = 0 m/s
When the car is moving away from you:
fr = 65 Hz
vr = 0 m/s
c, vs, and fs are constant.
We can write two equations:
76 = fs c / (c − vs)
65 = fs c / (c + vs)
If we divide the two equations:
76/65 = [fs c / (c − vs)] / [fs c / (c + vs)]
76/65 = [fs c / (c − vs)] × [(c + vs) / (fs c)]
76/65 = (c + vs) / (c − vs)
76 (c − vs) = 65 (c + vs)
76c − 76vs = 65c + 65vs
11c = 141vs
vs = 11/141 c
Substitute into either equation to find fs.
65 = fs c / (c + 11/141 c)
65 = fs c / (152/141 c)
65 = 141/152 fs
fs = 70 Hz
