First slide

Stationary waves

Question

Two closed organ pipes of length 100 cm and 101 cm 16 beats in 20 sec. When each pipe is sounded in its fundamental mode calculate the velocity of sound

Moderate

A

303 ms^–1
B

332 ms^–1
C

323.2 ms^–1
D

300 ms^–1

Solution

Number of beats per second,
$n = \frac{16}{20} = \frac{4}{5} \Rightarrow n = n_{1} - n_{2} = \frac{v}{4} (\frac{1}{l_{1}} - \frac{1}{l_{2}})$
$\Rightarrow \frac{4}{5} = \frac{v}{4} (\frac{1}{1} - \frac{1}{1 .01}) = \frac{0 .01 v}{4 \times 1 .01}$
$v = \frac{16 \times 101}{5} = 323 .2 {ms}^{- 1}$

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