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JEE Main 2024 (6 Apr, Shift 2) · Organ Pipes & Resonance Tube

Organ Pipes & Resonance Tube question from JEE Main 2024 (6 Apr, Shift 2)

Q54JEE Main 2024 · 6 APR · SHIFT 2Medium

Organ Pipes & Resonance Tube

Two open organ pipes of lengths $60\text{ cm}$ and $90\text{ cm}$ resonate at $6$ th and $5$ th harmonics respectively. The difference of frequencies for the given modes is _________ $\text{Hz}$ . (Velocity of sound in air $= 333\text{ m/s}$ )

Numerical answer type. Work it out, then open the answer.

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Answer: 740

Open pipe: $f_n = \frac{nv}{2L}$ .
$f_6 = \frac{6 \times 333}{2 \times 0.6} = 1665\text{ Hz}$
$f_5 = \frac{5 \times 333}{2 \times 0.9} = 925\text{ Hz}$
Difference $= 1665 - 925 = 740\text{ Hz}$

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