Question

A longitudinal sound wave given by $p=2.5sin\frac{\pi }{2}(x-600t)$ (P is in $N/m^2$ and x is in metre and t is in second) is sent down a closed organ pipe. If the pipe vibrates in its second overtone, the length of the pipe is

• A. 6 m
• B. 8 m
• C. 5 m
• D. 106 m

Answer 1

The correct option is C 5 m

The second overtone $\frac{5\lambda }{4}=L$...(i)

where $\lambda$ is wavelength of sound wave which is given as $\lambda =\frac{2\pi }{k}=\frac{2\pi }{\frac{\pi }{2}}=4m$

From equation (i)

$L=\frac{5\lambda }{4}=\frac{5\times 4}{4}=5m$