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

$\begin{array}{l}Speed of sound in a gas =V=\sqrt{\frac{B}{\rho }}\text{}\\ \therefore \frac{V_{pipe}}{V_{air}}=\frac{\sqrt{\frac{B}{2\rho }}}{\sqrt{\frac{B}{\rho }}}=\frac{1}{\sqrt{2}}\\ \Rightarrow V_{pipe}=\frac{V_{air}}{\sqrt{2}}=\frac{300}{\sqrt{2}}m/s\text{}\\ Now, frequency in open organ pipe =f_n=\frac{\left(n+1\right)V_{pipe}}{2l}\\ Fundamental frequency =f_0=\frac{V_{pipe}}{2l}\\ \text{}Second Harmony = f_1=\frac{2V_{pipe}}{2l}\\ Thus, frequency difference =f_1-f_0=\frac{V_{pipe}}{2l}=\frac{300}{2\sqrt{2}}=106.38Hz \left(If\sqrt{2}=1.41\right)\\ or{f}_1-f_0=106.08Hz \left(If\sqrt{2}=1.414\right)\end{array}$