You are driving a car and you hear the sound of the engine of a car approaching

Question

You are driving a car and you hear the sound of the engine of a car approaching from behind.

a) The frequency of the engine of the other car approaching from behind you is 130 Hz. After that other car passed your car, the frequency that you hear is 120 Hz. If your car was moving with speed 50 mph find the speed of the other car. Assume that both cars are moving with constant speed. Assume that the sound is c = 340.29 m/s and that there is no wind.

b) What is the original frequency of the engine of the other car?

c) How would your reslut from part (a) change if there is a 10 mph wind blowing in the opposite direction from the velocity of your car? Everything else is the same as part (a). Solve for the speed of the other car.

Explanation / Answer

(a)
f = 130 Hz
vo = 50 mph = 22.35 m/s
Let the original frequency of the engine of the other car be f.

While approaching,
130 = f * (340.3 - 22.35) / (340.3 - vs )

When the car has passed,
120 = f * (340.3 + 22.35) / (340.3 + vs )

Solving the two eq,
vs = 35.86 m/s = 80.2 mph
f = 124.5 Hz

(a) Speed of the other car, vs = 80.2 mph
(b) original frequency of the engine of the other car, f = 124.5 Hz
(c)
The speed of sound increases or decreases according to direction of wind. If windis blowing in direction of propagation of sound , the speed of sound increases , while if it is blowing in a direction opposite to that of sound ,the speed of sound decreases.

While approaching,
130 = f * (340.3 - 4.47 - 22.35) / (340.3 - 4.47 - vs )

When the car has passed,
120 = f * (340.3 + 4.47 + 22.35) / (340.3 + 4.47 + vs )

solving the two eq,
vs = 35.83 m/s
vs = 80.14 mph

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