# What is the frequency heard by a person driving at 15 m/s toward a blowing factory whistle (800. Hz) if the speed of sound is 340.6 m/s?

Jun 8, 2018

840 Hz

(P.S. this is rounded to 2 s.f)

#### Explanation:

We use the formula
${f}_{o}$ = (v.${f}_{s}$)/(v-${v}_{p}$)

Here, '${f}_{o}$' means observed frequency, 'v' means speed of sound in air, '${f}_{s}$' means frequency of the source (blowing factory whistle) and '${v}_{p}$' is the speed of the person moving towards the whistle.

Since the person is moving towards the whistle the velocities are subtracted.

The observed frequency is higher than the frequency of the whistle because the person is moving closer, so the observed wavelength is smaller. Wavelength is inversely proportional to frequency based on this formula (v=λf). So frequency should be higher.

By substituting the values, you should be able to find the answer.

${f}_{o}$= (340.6×800)÷(340.6-15)= 836.9 Hz