Chapter 12, Problem 41P

To determine

The operating frequency of brand X.

Answer to Problem 41P

  $f=28.5\text{ kHz}$ .

Explanation of Solution

Given:

Whistle frequency ( f_w ) = 23.5 kHz,

Shrill wine frequency ( f_S )= 5000 Hz. = 5 kHz

Formula used:

  $f=f_w\pm f_s\text{ kHz}\text{.}$

Calculation: 

The two whistles are played simultaneously, the beats can be heard and the beat frequency is the difference between the given frequencies of whistle and shrill whine.

  $f=f_w\pm f_s\text{ kHz}\text{.}$

  $f=23.5\pm 5\text{ kHz}\text{.}$$$

  $f=23.5-5\text{ kHz}$ and $f=23.5+5\text{ kHz}\text{.}$

  $f=18.5\text{ kHz}$ or $f=28.5\text{ kHz}$

The operating frequency of brand X should be more than the 23.5 kHz to hear the sound. Therefore, it should be (23.5+5) = 28.5 kHz.

Conclusion: 

The operating frequency of brand X is 28.5 kHz. So, the human can hear the sound.