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.
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
