First slide

Standing waves

Question

A closed organ pipe has length ' $l$ '. The air in it is vibrating in 3rd overtone with rnaximum amplitude 'a'. The amplitude at a distance of $\frac{l}{7}$ from closed end of the pipe.

Moderate

A

a
B

$\frac{a}{2}$
C

$\frac{\sqrt{3}}{2} a$
D

$\frac{1}{\sqrt{2}} a$

Solution

The figure shows variation of displacement of particles in a closed organ pipe for 3rd overtone.
For third overtone $l = \frac{7 λ}{4} or λ = \frac{4 l}{7} or \frac{λ}{4} = \frac{l}{7}$
Hence the amplitude at P at a distance $\frac{l}{7}$ from closed end is 'a' because there is an antinode at that point.

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