Question

In an organ pipe whose one end is at x = 0, the pressure is expressed by
$\rho ={\rho }_{0}cos\frac{3\pi x}{2}sin300\pi t$ where x is in meter and t in sec. The organ pipe can be

• A. closed at one end, open at another with length = 0.5 m
• B. open at both ends, length = 1 m
• C. closed at both ends, length = 2 m
• D. closed at one end, open at another with length = $\frac{2}{3}m$

Answer 1

The correct option is C closed at both ends, length = 2 m

Pressure is maximum at closed end and minimum at open end.

At $x=0m$, $cos\frac{3\pi x}{2}=cos\frac{3\pi \times 0}{2}=1$

Thus $p$ is maximum, so $x=0$ is a closed end

At $x=2m$ $cos\frac{3\pi x}{2}=cos\frac{3\pi \times 2}{2}=-1$

Thus $|p|$ is maximum at $x=2m$, so $x=2$ is also a closed end.

Hence the given organ pipe is closed at both ends and length of the pipe is $2m$