Question

A longitudinal sound wave given by $p=5\sin \frac{\pi }{3}(x-400t)$ ($p$ is in ${\text{N/m}}^2$, $x$ is in metres and $t$ is in seconds) is sent down a closed organ pipe. If the pipe vibrates in its second overtone, the length of the pipe is

• A. $7.5\text{m}$
• B. $15\text{m}$
• C. $5\text{m}$
• D. $2\text{m}$

Answer 1

The correct option is A $7.5\text{m}$

Given that
$p=5\sin \frac{\pi }{3}(x-400t)$
From equation,
$k=\frac{\pi }{3}$
So, wavelength $\left(\lambda \right)=\frac{2\pi }{k}=\frac{2\pi }{\frac{\pi }{3}}=6\text{m}$
For second overtone,
$l=\frac{\lambda }{4}+\frac{\lambda }{2}+\frac{\lambda }{2}=\frac{5\lambda }{4}=\frac{5}{4}\times 6$
$\Rightarrow l=7.5\text{m}$