Verified Solution • 2025–26 Session moderate

QJEEM20Phdb6e: JEE Main 2020 Physics - Class 11 JEEM20Phdb6e Solution: A one metre long (both ends open) organ pipe is kept in a gas…

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 300 m/s, the frequency difference between the fundamental and second harmonic of this pipe is ________ Hz.

Step-by-Step Verified Solution

Velocity of sound v = Bρ\sqrt {{B \over \rho }}

∴\therefore vpipevair=B2ρBρ{{{v_{pipe}}} \over {{v_{air}}}} = \sqrt {{{{B \over {2\rho }}} \over {{B \over \rho }}}}

⇒\Rightarrow vpipe = vair2{{{{v_{air}}} \over {\sqrt 2 }}} = 3002{{{300} \over {\sqrt 2 }}} = 150 2{\sqrt 2 }

We know, for open organ pipe

fn = (n+1)vpipe2l\left( {n + 1} \right){{{v_{pipe}}} \over {2l}}

Difference between 2nd and fundamental frequency

f1 - f0 = vpipe2l{{{v_{pipe}}} \over {2l}} = 15022(1){{150\sqrt 2 } \over {2\left( 1 \right)}} = 106.06 Hz

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