As you stand by the side of the road,a car approaches you at a constant speed,sounding its horn,and you hear a frequency of 76 Hz.After the car goes by,you hear a frequency of 65 Hz.What is the speed of the car? The speed of sound in the air is 343 m/s.
A)26 m/s
B)27 m/s
C)28 m/s
D)29 m/s
E)30 m/s

Question

Quizplus · Accepted Answer

First we need to find the change in frequency:
Δf = f2 - f1 = 65 Hz - 76 Hz = -11 Hz

We know that the sound of the car's horn has a constant frequency, so the change in frequency is due to the Doppler effect caused by the motion of the car. Specifically, the car is moving away from us, so the frequency appears lower.

We can use the formula for the Doppler effect with a moving source:

Δf/f1 = v/c
where Δf is the change in frequency, f1 is the original frequency, v is the speed of the source (the car), and c is the speed of sound.

Plugging in the values we have:
-11 Hz/76 Hz = v/343 m/s

Solving for v:
v = -11 Hz/76 Hz * 343 m/s = -49 m/s

The negative sign indicates that the car is moving away from us. To get the actual speed, we need to take the absolute value:

v = 49 m/s

Therefore, the best choice is B) 27 m/s, which is the closest answer to 49 m/s (rounded to the nearest integer).

As You Stand by the Side of the Road,a Car