Question

A pipe of length $l_1$ closed at one end is kept in a chamber of gas of density ${\rho }_2$. A second pipe open at both ends is placed in a second chamber of gas density ${\rho }_2$. The compressibility of both gases are equal. If frequency of First overtone in both the cases are equal and length of second pipe is given by $N{l}_1$ then find value of N. (given ${\rho }_1=27kg/m^3,{\rho }_2=3kg/m^3$)

Answer 1

We got $l_2=\frac{4}{3}{l}_1\sqrt{\frac{{\rho }_1}{{\rho }_2}}$

$\Rightarrow L_2=4l_1$

$\Rightarrow N=4$