Question

48) A motorcycle and a police car are moving toward one another. The police car emits sound with a frequency of 523 Hz and has a speed of 32.2 m/s. The motorcycle has a speed of 14.8 m/s. What frequency does the motorcyclist hear?

Answer 1

`602.1Hz`

Step-by-step explanation

To find the frequency that the motorcyclist hears, we have to apply the rules of the Doppler effect. Doppler effect describes the change in perceived frequency of a wave based on the observer and the source of the wave.

For an object moving toward the source of the wave, we have that the frequency is:

`f^(\prime)=((v+v_0))/((v-v_s))f`

where v = velocity of sound waves

v0 = velocity of motorcyclist

vs = velocity of source of sound

f = frequency

Therefore, substituting the given values, we have that the frequency that the motorcyclist hears is:

`\begin{gathered} f^(\prime)=(343+14.8)/(343-32.2)\cdot523 \\ f^(\prime)=(357.8)/(310.8)\cdot523 \\ f^(\prime)=602.1Hz \end{gathered}`

That is the answer.