First slide

Stationary waves

Question

A one meter long (both ends open) organ pipe is kept in a gas that has triple the density of air at STP. Assuming the speed of sound in air at S.T.P is 300 m/s . The frequency difference between the fundamental and second harmonic of this pipe is

Moderate

A

105 Hz
B

86.60 Hz
C

100 Hz
D

109.02 Hz

Solution

$W e k n o w t h a t s p e e d o f s o u n d i s g i v e n b y V_{S} = \sqrt{\frac{γ P}{ρ}} ∴ \frac{V_{g a s}}{V_{a i r}} = \sqrt{\frac{ρ_{a i r}}{ρ_{g a s}}} \Rightarrow \frac{V_{g a s}}{300} = \frac{1}{\sqrt{3}} \Rightarrow V g a s = \frac{300}{\sqrt{3}} N o w, D i f f e r e n c e i n f r e q u e n c y = n_{2} - n_{1} = \frac{V_{g a s}}{2 l} = \frac{300}{\sqrt{3} \times 2 \times 1} = 86.60 H z$

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