Two open organ pipes of length $60 \mathrm{~cm}$ 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 $=333 \mathrm{~m} / \mathrm{s}$ )
JEE MAIN 2024, Diffcult
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The difference in frequency in open organ pipe $=$
$\mathrm{f}=\frac{\mathrm{nv}}{2 \mathrm{~L}}$
$\Delta \mathrm{f}=\frac{6 \mathrm{v}}{2 \times 0.6}-\frac{5 \mathrm{v}}{2 \times 0.9}$
$\mathrm{v}=333 \mathrm{~m} / \mathrm{s}$
$\Delta \mathrm{f}=740 \mathrm{~Hz}$
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