Q82 / 90 · JEE Main 2024 (06 Apr Shift 2) · Physics

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

Correct answer: 740

Solution

The difference in frequency in open organ pipe $=$ $\begin{aligned} & \mathrm{f}=\frac{\mathrm{nv}}{2 \mathrm{~L}} \\ & \Delta \mathrm{f}=\frac{6 \mathrm{v}}{2 \times 0.6}-\frac{5 \mathrm{v}}{2 \times 0.9} \\ & \mathrm{v}=333 \mathrm{~m} / \mathrm{s} \\ & \Delta \mathrm{f}=740 \mathrm{~Hz} \end{aligned}$

Hence, the correct answer is 740.

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