Chapter 15, Problem 74A

To determine

To write: A physics problem with real life objects for which the following equation would be a part of the solution:

  $440\text{ Hz}=\frac{442\text{ Hz(343 m/s}-v_2)}{\text{343 m/s}}$

Explanation of Solution

Introduction:

The Doppler’s effect equation is given by:

$f_d=f_s\left(\frac{v-v_d}{v-v_s}\right)$

Where $f_s$ is frequency of the source, $v$ is the speed of sound in air, $v_d$ is velocity of the detector and $v_s$ is velocity of the source.

The given solution is a part of Doppler’s effect equation. So a problem based on Doppler’s effect for which the given solution would be a part of can be:

A truck at rest is blowing a horn with a frequency of $442\text{ Hz}$ . A car moving away from the truck hears the sound with a frequency of $440\text{ Hz}$ . Find the velocity of the car.

Conclusion:

Substituting the values of $f_d=440\text{ Hz}$ , $f_s=442\text{ Hz}$ , $v_s=0$ , $v=343\text{ m/s}$ , the required solution is obtained:

$440\text{ Hz}=442\text{ Hz}\left(\frac{343\text{ m/s}-v_d}{343\text{ m/s}}\right)$