Chapter 15.1, Problem 3PP

To determine

To find: the frequency of sound perceived by an automobile driver from another automobile.

Answer to Problem 3PP

The frequency of sound perceived by the automobile driver from another automobile is $475\text{ Hz}$ .

Explanation of Solution

Given information:

Speed of sound in air at ( $v$ ) = $+343\text{ m/s}$

Velocity of second automobile (source) ( $v_s$ ) = $\mathrm{24.6.0}\text{ m/s}$

Velocity of first automobile (detector) ( $v_d$ ) = $\mathrm{24.6.0}\text{ m/s}$

Frequency of wave ( $f_s$ ) = $\text{475 Hz}$

Both the automobile are moving towards each other.

Formula Used:

As per, Doppler Effect equation:

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

Where $f_d$ represents frequency perceived by the detector, $f_s$ represents wave’s frequency, $v$ represents speed of sound in air, $v_s$ represents velocity of source and $v_d$ represents velocity of detector.

Calculations:

Now putting value of $f_s=475\text{ Hz}$ , $v=343\text{ m/s}$ , $v_s=24.6\text{ m/s}$ and $v_d=24.6\text{ m/s}$ , we get

  $f_d=475\text{ Hz}$

Conclusions:

Frequency perceived by the detector

  $f_d=475\text{ Hz}$

That is,

Frequency perceived by the detector is equal to the frequency of the source.