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  • 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 , the frequency differ

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, the frequency difference between the fundamental and second harmonic of this pipe is ________Hz. 
Option: 1 106
Option: 2 600
Option: 3 310
Option: 4 210
 

Answers (1)

best_answer

 

 

   

 

\begin{array}{l}{\mathrm{V}=\sqrt{\frac{\mathrm{B}}{\rho}}} \\\\ {\frac{\mathrm{V}_{\text {pipe }}}{\mathrm{V}_{\text {air }}}=\frac{\sqrt{\frac{\mathrm{B}}{2 \rho}}}{\sqrt{\frac{\mathrm{B}}{ \rho}}}=\frac{1}{\sqrt{2}}} \\\\ {\mathrm{V}_{\text {pipe }}=\frac{V_{\text {air }}}{\sqrt{2}}}\end{array}

\begin{array}{l}{f_{n}=\frac{(n+1) V_{\text {pipe }}}{2 \ell}} \\ {\left.f_{1}-f_{0}=\frac{V_{\text {pipe }}}{2 \ell}=\frac{300}{2 \sqrt{2}}=106.38 =106\ \mathrm{Hz} \text { (If } \sqrt{2}=1.41\right)}\end{array}

So the answer will be 106

Posted by

vishal kumar

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