First slide

Standing waves

Question

The air column in a closed organ pipe of length 25 cm is oscillating in second overtone when a standing wave is produced in it. Ignoring end effect, find the minimum distance from the open end of the tube where variation of pressure is maximum.

Moderate

A

5 cm
B

3 cm
C

10 cm
D

8 cm

Solution

Frequency of second over tone, $f = 5 . \frac{v}{4 l}$
$∴$ Wave length $λ = \frac{v}{f} = \frac{4 l}{5}$
Maximum variation of pressure takes place at node
$∴$ Minimum distance $= \frac{λ}{4} = \frac{l}{5} = \frac{25}{5} c m = 5 c m$

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