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Damped Oscillations

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Question

There is a set of tuning forks, one with the lowest frequency vibrating at 550 Hz. By using any two tuning forks at a time, the following beat frequencies are heard : 1, 2, 3, 5, 7, 8. The possible frequencies of the other three forks are:

A

552Hz, 553Hz, 580Hz

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B

557Hz, 558Hz, 600Hz

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C

555Hz, 553Hz, 558Hz

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D

551Hz, 553Hz, 558Hz

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Solution

The correct option is C 551Hz, 553Hz, 558Hz
When two or more sine waves are combined, there are components found that are the sum and difference of the waves. The differences or difference is where the beats are found.

Beat frequency $= f_{1} - f_{2}$
So the possible frequencies of the other three forks are: 551 Hz, 553 Hz and 558 Hz
558 - 550 = 8 Hz
558 - 551 = 7 Hz
558 - 553 = 5 Hz
553 - 550 = 3 Hz
553 - 551 = 2 Hz
551 - 550 = 1 Hz

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