JEE Main · 2022 · 27 Jul 2022 · Shift 2 · Waves & Sound

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A wire of length 30 cm, stretched between rigid supports, has it's nᵗʰ and (n+1)ᵗʰ harmonics at 400 Hz and 450 Hz, respectively. If tension in the string is 2700 N, it's linear mass density is ______ kg/m.

Answer: 3

Solution

For a string fixed at both ends, the nth harmonic frequency is:

f_{n} = \frac{n v}{2 L}

Given:

f_{n} = 400

Hz and

f_{n + 1} = 450

Hz, with

L = 0.3

\frac{n v}{0.6} = 400 and \frac{( n + 1 ) v}{0.6} = 450

Subtracting:

\frac{v}{0.6} = 50 ⟹ v = 30 m/s

The wave speed on a string is:

v = \frac{T}{μ}

30 = \frac{2700}{μ} ⟹ 900 = \frac{2700}{μ} ⟹ μ = 3 kg/m

Answer: 3

JEE Main · 2022 · 27 Jul 2022 · Shift 2 · Integer answer

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