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JEE Main 20208 JanuaryMorning Shift
Exam
JEE Main
Year
2020
Date
8 January
Shift
Morning Shift
Subject
Physics
Chapter
Waves and Sound

JEE Main 2020 · 8 January · Morning Shift · Physics · Waves and Sound

A one metre long (both ends open) organ pipe is kept in a gas that...

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.

Correct answer

0

Step-by-step solution

V=BρV = \sqrt{\dfrac{B}{ρ}}
VpipeVair=B2ρBρ=12\dfrac{{V}_{pipe}}{{V}_{air}} = \dfrac{\sqrt{\dfrac{B}{2ρ}}}{\sqrt{\dfrac{B}{ρ}}} = \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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