First slide

Stationary waves

Question

Two closed organ pipes, when sounded simultaneously gave 4 beats per sec. If longer pipe has a length of 1m. Then length of shorter pipe will be, (v = 300 m/s)

Moderate

A

185.5 cm
B

94.9 cm
C

90 cm
D

80 cm

Solution

For first pipe $n_{1} = \frac{v}{4 l_{1}}$ and for second pipe $n_{2} = \frac{v}{4 l_{2}}$
So, number of beats = $n_{2} - n_{1} = 4$
$\Rightarrow 4 = \frac{v}{4} (\frac{1}{l_{2}} - \frac{1}{l_{1}}) \Rightarrow 16 = 300 (\frac{1}{l_{2}} - \frac{1}{1}) \Rightarrow l_{2} = 94 .9 cm$

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