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.
Answer (integer)
105
Solution
Velocity of sound v = $\sqrt {{B \over \rho }}$
<br><br>$\therefore$ $${{{v_{pipe}}} \over {{v_{air}}}} = \sqrt {{{{B \over {2\rho }}} \over {{B \over \rho }}}} $$
<br><br>$\Rightarrow$ v<sub>pipe</sub> = ${{{{v_{air}}} \over {\sqrt 2 }}}$ = ${{{300} \over {\sqrt 2 }}}$ = 150${\sqrt 2 }$
<br><br>We know, for open organ pipe
<br><br>f<sub>n</sub> = $\left( {n + 1} \right){{{v_{pipe}}} \over {2l}}$
<br><br>Difference between 2<sup>nd</sup> and fundamental frequency
<br><br>f<sub>1</sub> - f<sub>0</sub> = ${{{v_{pipe}}} \over {2l}}$ = ${{150\sqrt 2 } \over {2\left( 1 \right)}}$ = 106.06 Hz
About this question
Subject: Physics · Chapter: Waves · Topic: Wave Motion and Types
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