First slide

Stationary waves

Question

An open pipe is in resonance in its 2^nd harmonic with tuning fork of frequency f₁. Now it is closed at one end. If the frequency of the tuning fork is increased slowly from
f₁ then again a resonance is obtained with a frequency f₂ . If in this case the pipe vibrates n^th harmonics then

Moderate

A

$n = 3, f_{2} = \frac{3}{4} f_{1}$
B

$n = 3, f_{2} = \frac{5}{4} f_{1}$
C

$n = 5, f_{2} = \frac{5}{4} f_{1}$
D

$n = 5, f_{2} = \frac{3}{4} f_{1}$

Solution

Open pipe resonance frequency $f_{1} = \frac{2 v}{2 L}$
Closed pipe resonance frequency $f_{2} = \frac{n v}{4 L}$
$f_{2} = \frac{n}{4} f_{1} (where n is odd and f_{2} > f_{1})$
$∴ n = 5$

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