Two open organ pipes of lengths 60 cm and 90 cm resonate at 6th and 5th harmonics respectively. The difference of frequencies for the given modes is ____ Hz

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Solution

Q.
Two open organ pipes of lengths 60 cm and 90 cm resonate at 6th and 5th harmonics respectively. The difference of frequencies for the given modes is ____ Hz

(Velocity of sound in air = 333 m/s) [2024]

Ans.
(740)

For first open organ pipe

$f = \frac{n v}{2 l} \Rightarrow f_{6} = \frac{6 v}{2 l_{1}}$

$f_{6} = \frac{6 v}{2 (0.6)} = 5 v$ ...(i)

For second open organ pipe

$f_{5} = \frac{5 v}{2 (l_{2})} = \frac{5 v}{2 (0.9)} = \frac{25}{9} v$ ...(ii)

$Δ f = f_{6} - f_{5} = 5 v - \frac{25 v}{9}$

$Δ f = \frac{(45 - 25) v}{9} = \frac{20}{9} v = \frac{20}{9} \times 333 \Rightarrow Δ f = 740 Hz$

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