Q 11-14-103JEE MainJEE Main 2020 (8 Jan, Shift 1)Medium
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.
Numerical value type. Enter your answer.
Answer: 106
At the same pressure, $v \propto \dfrac{1}{\sqrt\rho}$, so in the gas $v = \dfrac{300}{\sqrt2} \approx 212$ m/s.
For an open pipe $f_n = \dfrac{nv}{2L}$, so
$$f_2 - f_1 = \frac{v}{2L} = \frac{212}{2} \approx 106\ \text{Hz}$$
Solution by Sreeraj P, M.Sc Physics