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 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

The formula to find the speed of the car is:

v = (f2 - f1) / (f2 + f1) * v_sound

where v is the speed of the car, f1 is the initial frequency (76 Hz), f2 is the final frequency (65 Hz), and v_sound is the speed of sound in air (343 m/s).

Plugging in the values gives:

v = (65 - 76) / (65 + 76) * 343
v ≈ -0.101 * 343
v ≈ -34.7 m/s

Note that the negative value indicates that the car is moving away from the observer. We can take the absolute value to get the speed:

|v| ≈ 34.7 m/s

Therefore, the correct answer is B) 27 m/s, which is the closest choice to the calculated value of 34.7 m/s.

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