A tuning fork gives 3 beats with 50 cm length of sonometer wire. If the length of the wire is shortened by 1 cm, the number of beats is still the same. The frequency of the fork is (a) 256 Hz (b) 288 Hz (c) 297 Hz (d) 320 Hz

Answer: (c). f ∝ 1/L: 50 cm wire gives n - 3, 49 cm wire gives n + 3. (n - 3) × 50 = (n + 3) × 49 50n - 150 = 49n + 147 ⇒ n = 297 Hz So the answer is (c) 297 Hz.

A tuning fork gives 3 beats with 50 cm length of sonometer wire. If… | MHT CET 2023 (12 May, Shift 2)

Q43MHT CET 2023 · 12 MAY · SHIFT 2Medium

Beats

A tuning fork gives 3 beats with $50\text{ cm}$ length of sonometer wire. If the length of the wire is shortened by $1\text{ cm}$ , the number of beats is still the same. The frequency of the fork is

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Answer: (c)

$f \propto \dfrac{1}{L}$ : 50 cm wire gives $n - 3$ , 49 cm wire gives $n + 3$ .
$(n - 3) \times 50 = (n + 3) \times 49$
$50n - 150 = 49n + 147 \Rightarrow n = 297\text{ Hz}$
So the answer is (c) 297 Hz.

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