JEE PYQ: Waves And Sound Question 1
Question 1 - 2021 (16 Mar Shift 2)
A closed organ pipe of length L and an open organ pipe contain gases of densities $\rho_1$ and $\rho_2$ respectively. The compressibility of gases are equal in both the pipes. Both the pipes are vibrating in their first overtone with same frequency. The length of the open pipe is $\frac{x}{3}L\sqrt{\frac{\rho_1}{\rho_2}}$ where $x$ is __________. (Round off to the Nearest Integer)
Show Answer
Answer: 4
Solution
$f_c = f_o$
$\frac{3V_c}{4L} = \frac{2V_o}{2L’}$
$\frac{3V_c}{4L} = \frac{V_o}{L’}$
$L’ = \frac{4L}{3} \cdot \frac{V_o}{V_c} = \frac{4L}{3}\sqrt{\frac{B/\rho_1}{B/\rho_2}}$ (B is bulk modulus)
$= \frac{4L}{3}\sqrt{\frac{\rho_1}{\rho_2}}$
$x = 4$
BETA
