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. 38 Hz and 63 Hz
B. 22 Hz and 42 Hz
C. 47 Hz and 55 Hz
D. 18 Hz and 26 Hz

Answer 1

The right answer for the question that is being asked and shown above is that: "B. 22 Hz and 42 Hz." If 20 beats are produced within one second, the frequencies that could possibly be held by two sound waves traveling through a medium along a common path at the same time is B. 22 Hz and 42 Hz

Answer 2

B. 22 Hz and 42 Hz

Step-by-step explanation:

The beat is an interference pattern which occurs when two waves of slightly different frequencies meet each other. The beat is heard as a periodic variation, whose frequency (called beat frequency) is equal to the absolute value of the difference between the frequencies of the individual waves:

`f_B = |f_1-f_2|`

In this problem, we are told that 20 beats per second are produced, so the beat frequency is

`f_B = 20 s^(-1) = 20 Hz`

Therefore, we must find the two waves which have a difference in frequency equal to this value, 20 Hz. Let's see each choice:

A. 38 Hz and 63 Hz -->
`f_B = |38 Hz-63 Hz|=25 Hz` --> NO

B. 22 Hz and 42 Hz -->
`f_B = |22 Hz-42 Hz|=20 Hz` --> YES

C. 47 Hz and 55 Hz -->
`f_B = |47 Hz-55 Hz|=8 Hz` --> NO

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

So, the correct choice is

B. 22 Hz and 42 Hz