Chapter 12, Problem 54P

To determine

To find: The frequency, that the bat can hear in the reflected wave.

Answer to Problem 54P

  $f^1=30.88\text{ kHz}$ .

Explanation of Solution

Given:

Speed of files towards a wall $\left(v_s\right)$ $=5\text{ m/s,}$

Frequency $\left(f\right)$ $=30\text{ kHz}=30000\text{ Hz}.$

Formula used:

Write the expression for the frequency as per Doppler effect.

  $f^1=f\left(\frac{v+v_s}{v-v_s}\right)\text{ Hz}$ .

  $v$ and $v_s$ = speed of wave and speed of source respectively.

Calculation:

  $v=343\text{ m/s,}$

and $v_s=5\text{ m/s}.$

Substitute the values in the equation,

  $f^1=30000\times \left(\frac{343+5}{343-5}\right)\text{ Hz}$

  $f^1=30887.57\text{ Hz}$

  $f^1=30.88\text{ kHz}$

Conclusion:

The frequency that is reflected to the bat is $30.88\text{ kHz}.$