Question

Four tuning forks of frequencies 200, 201, 204 and 206 Hz are sounded together. The beat frequency will be-
(A)6
(B)12
(C) 15
(D)None of these

Answer 1

Here there are four sources so in order to find overall beat frequency you need to find beat frequency of each combination and then take the LCM of beat frequency of each combination to find the final beat frequency.

Complete step by step solution:
There are four source of frequency so there will be $^4{C_2} = 6$ combinations
Those combinations are (200,201),(200,204),(200,206),(201,204),(201,206) and (204,206)
Now we will find the beat of each combination. Which is given by the difference between the combination.
beat frequency of (200,201) will be 1,
beat frequency of (200,204) will be 4,
beat frequency of (200,206) will be 6,
beat frequency of (201,204) will be 3,
beat frequency of (201,206) will be 5 and
beat frequency of (204,206) will be 2.
Now,
The beat frequencies are-1,4,6,3,5 & 2. As the final beat frequency will be the LCM of all the beat frequencies obtained and LCM of all these will be 30.
Hence, the final beat frequency will be 30.

Therefore, Option-D is correct.

Note: when there are more than two sources keep in mind that each pair will have different beat frequency and net beat frequency will occur when all the different beat frequencies of each pair are in sync. and all the beat frequencies will be in sync when we take the LCM so simply take LCM of beat frequencies of each pair and you will get the answer.