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Waves

JEE Main level, single correct, medium

81 of 142

Question 81 of 142

In an open organ pipe $\nu_{3}$ and $\nu_{6}$ are $3^{\text {rd }}$ and $6^{\text {th }}$ harmonic frequencies, respectively. If $\nu_{6}-\nu_{3}=2200 \mathrm{~Hz}$ then length of the pipe is $\_\_\_\_$ mm . (Take velocity of sound in air is $330 \mathrm{~m} / \mathrm{s}$ .)

Show answer and solution

Answer: (C) 225

For an open organ pipe, the

n

-th harmonic frequency is

f_n = n \cdot \frac{v}{2L}

.
The 3rd harmonic is

v_3 = 3 \cdot \frac{330}{2L}

and the 6th harmonic is

v_6 = 6 \cdot \frac{330}{2L}

.
Taking the difference:

v_6 - v_3 = (6-3) \cdot \frac{330}{2L} = 3 \cdot \frac{330}{2L} = 2200

.
Solving for

L

L = \frac{3 \times 330}{2 \times 2200} = \frac{990}{4400} = 0.225

m = 225 mm.

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JEE Main 2025 Apr 2 Shift 1 question paper

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