A sonometer wire of length 25 ~cm vibrates in unison with a tuning fork. When its length in decreased by 1 ~cm, 6 beats are heard per second. What is the frequency of the tuning fork?

Q138 / 150 · MHT CET 2021 (23 Sep Shift 1) · Physics

A sonometer wire of length $25 \mathrm{~cm}$ vibrates in unison with a tuning fork. When its length in decreased by $1 \mathrm{~cm}, 6$ beats are heard per second. What is the frequency of the tuning fork?

A
$200 \mathrm{~Hz}$
B
$72 \mathrm{~Hz}$
C
$100 \mathrm{~Hz}$
Correct answer
D
$144 \mathrm{~Hz}$

Solution

When length decrease, the frequency of wire will increase. If $n$ is the frequency of the tuning fork, then we have $$ \begin{aligned} & \mathrm{n} \times 25=(\mathrm{n}+6) \times 24 \\ & \therefore \mathrm{n}=144 \mathrm{~Hz} \end{aligned} $$

Hence, the correct answer is option: 'D'.

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