Question

1. A police car’s siren emits a sinusoidal wave with frequency of 300 Hz. The speed of sound is 340 m/s and the air is still.

a.) If a listener is at rest and the siren is moving away at 30 m/s, what frequency does the listener hear?

b.) If the siren is at rest and the listener is moving away from it at 30 m/s, what frequency does the listener hear?

2. The siren is moving away from the listener with a speed of 45 m/s relative to the air, and the listener is moving toward the siren with a speed of 15 m/s relative to the air. If the siren is emitting a 1kHz sound, what frequency does the listener hear?

Answer 1

The Doppler's effect equation says

$$f=f_0\frac{c\pm v_r}{c\pm v_s}$$

1a

$$f=\rm 300\: Hz*\frac{340\: m/s}{340\: m/s+30\: m/s}=276\: Hz$$

1b

$$f=\rm 300\: Hz*\frac{340\: m/s-30\: m/s}{340\: m/s}=274\: Hz$$

2

$$f=\rm 1000\: Hz*\frac{340\: m/s+15\: m/s}{340\: m/s+45\:m/s}=922\: Hz$$