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Beat Frequency

Ten tuning fo...

Question

Ten tuning forks are arranged in ascending order of their frequencies, each producing four beats per second with the preceding fork. If frequency of tenth fork is four times the frequency of the first fork, calculate the frequency of the first fork.

A

4 Hz

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B

18 Hz

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C

24 Hz

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D

12 Hz

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Solution

The correct option is D 12 Hz
We know that $f_{1} - f_{2} = 4, f_{2} - f_{3} = 4 f_{3} - f_{4} = 4 \dots$
$\Rightarrow 4 f = f + 9 \times 4 \Rightarrow f = 12 H z$

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