First slide

Stationary waves

Question

A one meter long (both ends open) organ pipe is kept in a gas that has double the density air at STP. Assuming the speed of sound in air at STP is $300 m / \sec$ . The frequency difference between the fundamental and second harmonic in this pipe is __________ Hz

Moderate

Solution

$S p e e d o f s o u n d i n g a s V_{S} = \sqrt{\frac{γ P}{ρ}} \frac{V g a s}{V a i r} = \sqrt{\frac{ρ a i r}{ρ g a s}} = \frac{1}{\sqrt{2}} V g a s = \frac{300}{\sqrt{2}} V g a s = 150 \sqrt{2} N o w n_{2} - n_{1} = \frac{V g a s}{2 l} = \frac{150 \sqrt{2}}{2 (1)} = 75 \sqrt{2} = 106.06 Δ n = 106.06 H z$

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