Question

Which tuning forks will give rise to a beat frequency of 20 Hz when sounded together with a 240 Hz tuning fork?

Answer 1

Use the concept of beat frequency to find the applicable final freqeuncy for 20Hz beat frequency.

Beat can be defined as 'the interference pattern between two sounds of slightly different frequencies0

The expression for beat frequency is given as

$f_{beat} = |f_1-f_2|$

Where,

$f_2 =$ Final frequency

$f_1 =$ Initial frequency

The beat frequency for us is 25Hz and the initial frequency is 240Hz, then

$20= |f_2-240|$

Being an absolute value, two values are possible, both in addition and subtraction:

$f_2 = 240 \pm 20$

The two possible values are

$f_2 = 220Hz$

$f_2 = 260Hz$