Question

The figure shows variation of displacement of particles in a closed organ pipe for $3^{rd}$ overtone. What is Amplitude at P. Diameter of pipe =2 m :

Answer 1

for closed end pipe $L=(2n+1)\frac{\lambda }{4}=(2\times 3+1)\frac{\lambda }{4}=\frac{7\lambda }{4}$

therefore $\frac{\lambda }{4}=\frac{l}{7}$

Hence the amplitude at P from the closed end at $\frac{l}{7}$ is a because of an antinode at that point.