First slide

Standing waves

Question

The air column in a one end closed tube is oscillating in first overtone with frequency 270 Hz. Now a tube of same diameter and length is joined to the open end of the closed tube so as to make a longer pipe closed at one end. Then the fundamental frequency of air column in the composite pipe is

Moderate

Solution

If $l$ be the length of the closed tube, then $f = 3 . \frac{v}{4 l}$
Length of the composite pipe is $2 l$ .
$∴$ $f'$ = Fundamental frequency = $\frac{v}{4 (2 l)} = \frac{1}{2} . \frac{f}{3} = \frac{270}{6} H z = 45 H z$

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