Question

While you are sitting outside you notice a police car driving away from you at 20 m/s. You know its siren normally sounds with a frequency of 440 Hz, but now it sounds about 415 Hz. What is the temperature outside?

A) 10°C
B) 15°C
C) 20°C
D) 25°C

Answer 1

The temperature outside is approximately 10°C. Option (A) is the correct answer.

Step-by-step explanation:

The observed decrease in the siren frequency (from 440 Hz to 415 Hz) is due to the Doppler effect. As the police car moves away from you, the sound waves are "stretched" out, leading to a perceived lower frequency. The amount of shift depends on the relative velocity between the source (siren) and the observer (you) and the speed of sound in the air.

We can use the Doppler effect equation to calculate the temperature:

f_observed = f_source * (v_sound - v_car) / v_sound

where:

f_observed is the observed frequency (415 Hz)

f_source is the source frequency (440 Hz)

v_sound is the speed of sound in air (which depends on temperature)

v_car is the car's velocity (20 m/s)

Solving for v_sound and then using the known relationship between sound speed and temperature, we can estimate the temperature to be around 10°C.

Option (A) is the correct answer. The other options (B, C, and D) represent higher temperatures, which would result in a smaller Doppler shift and a higher observed frequency.