Chapter 15.1, Problem 1PP

To determine

To find: the frequency of sound perceived by a detector from a trumpet player.

Answer to Problem 1PP

The frequency of sound perceived by a detector from a trumpet player is $489\text{ Hz}$ .

Explanation of Solution

Given information:

Speed of sound in air at ${20}^{\text{o}}\text{C}$ ( $v$ ) = $+343\text{ m/s}$

Velocity of car (source) ( $v_s$ ) = $24.6\text{ m/s}$

Velocity of detector ( $v_d$ ) = $0\text{ m/s}$ (at rest)

Frequency of wave ( $f_s$ ) = $524\text{ Hz}$

The car is moving away from the detector.

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 at ${20}^{\text{o}}\text{C}$ , $v_s$ represents velocity of source and $v_d$ represents velocity of detector.

Calculations:

As the car is moving away from the detector, so $v_s=-24.6\text{ m/s}$

Now putting value of $f_s=524\text{ Hz}$ , $v=343\text{ m/s}$ , $v_d=0\text{ m/s}$ and $v_s=-24.6\text{ m/s}$ , we get

  $f_d=489\text{ Hz}$

Conclusion:

Frequency perceived by the detector

  $f_d=489\text{ Hz}$