A truck moving at 36 m/s passes a police car moving at 45 m/s in the opposite direction. If the frequency of the siren is 500 Hz relative to the police car, what is the change in frequency (in Hz) heard by an observer in the truck as the two vehicles pass each other? (The speed of sound in air is 343 m/s.)

Question

Quizplus · Accepted Answer

First, we need to find the speed of sound as observed by the police car:
speed of sound relative to police car = speed of sound in air = 343 m/s

Next, we need to find the speed of sound as observed by the truck:
speed of sound relative to truck = speed of sound in air + speed of truck = 343 + 36 = 379 m/s

Now, we can use the formula for the Doppler effect:
change in frequency = (speed of sound + speed of observer)/(speed of sound + speed of source) * original frequency - original frequency
For an observer in the truck, the speed of sound is 379 m/s and the speed of the source (police car) is -45 m/s (since it is moving in the opposite direction), and the original frequency is 500 Hz:
change in frequency = (379 - (-45))/(379 + 343) * 500 - 500 = 240 Hz

Therefore, the answer is choice C.

A Truck Moving at 36 M/s Passes a Police Car