Waves

JEE Main level, numerical answer, medium

99 of 142

Question 99 of 142

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

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Answer: 106

V=BρV=\sqrt{\dfrac{B}{\rho }}
VpipeVair=B2ρBρ=12\dfrac{{V}_{pipe}}{{V}_{air}}=\dfrac{\sqrt{\dfrac{B}{2\rho }}}{\sqrt{\dfrac{B}{\rho }}}=\dfrac{1}{\sqrt{2}}
Vpipe=Vair2{V}_{pipe}=\dfrac{{V}_{air}}{\sqrt{2}}
fn=(n+1)Vpipe2l{f}_{n}=\dfrac{(n+1){V}_{pipe}}{2l}
f1−f0=Vpipe2l=30022=105.75Hz(if2=1.41){f}_{1}-{f}_{0}=\dfrac{{V}_{pipe}}{2l}=\dfrac{300}{2\sqrt{2}}=105.75Hz\left(if\sqrt{2}=1.41\right)
=106.05Hz(if2=1.414)=106.05Hz\left(if\sqrt{2}=1.414\right)

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