Question

A stationary whistle emits a sound of 180 Hz. If a car hears the whistle with a frequency of 200 Hz, how fast was it moving (in m/s)? Use 340 m/s for the sound velocity.

Answer 1

The speed of the car moving towards the stationary whistle, based on the Doppler Effect and the observed change in frequency from 180 Hz to 200 Hz, was calculated to be 34 meters per second.

Step-by-step explanation:

The student is encountering a scenario that is explained by the Doppler Effect, which describes the change in frequency of a wave in relation to an observer moving relative to the wave source. In this case, the frequency of the sound being heard is higher than the frequency of the sound being emitted, which indicates that the car is moving toward the stationary whistle. To find out how fast the car was moving, we can use the Doppler Effect formula for sound moving towards the observer:

f' = f * (v/(v - vs))

where:

• f' is the observed frequency (200 Hz),
• f is the emitted frequency (180 Hz),
• v is the speed of sound (340 m/s), and
• vs is the speed of the source (the car).

Rearranging the formula to solve for vs, we get:

vs = v*(1 - f/f')

Plugging in the given values:

vs = 340 m/s * (1 - 180 Hz / 200 Hz) = 340 m/s * (1 - 0.9) = 340 m/s * 0.1 = 34 m/s.

Thus, the speed of the car was 34 meters per second.