Question

If 20 beats are produced within one second, which of the following frequencies could possibly be held by two sound waves traveling through a medium along a common path at the same time
A. 22 Hz and 42 Hz
B. 47 Hz and 55 Hz
C. 38 Hz and 63 Hz
D. 18 Hz and 26 Hz?

Answer 1

Answer:

A. 22 Hz and 42 Hz

Explanation:

When two waves of slightly different frequency meet each other, they produce an interference pattern called beat. The frequency of this beat is equal to the absolute value of the difference between the individual frequencies of the two waves:

$f_B=|f_1-f_2|$

In this problem, we have 20 beats per second, so the beat frequency is

$f_B = \frac{20}{1 s}=20 Hz$

Therefore, we have to find the pair of waves whose frequency difference is 20 Hz. Let's analyze each choice:

A. $f_B = |22 Hz - 42 Hz|=20 Hz$ --> YES

B. $f_B = |47 Hz - 55 Hz|=8 Hz$ --> NO

C. $f_B = |38 Hz - 63 Hz|=25 Hz$ --> NO

D. $f_B = |18 Hz - 26 Hz|=8 Hz$ --> NO

So, the correct choice is A.