First slide

Stationary waves

Question

Two open organ pipes give 4 beats/sec when sounded together in their fundamental nodes. If the length of the pipe are 100 cm and 102.5 cm respectively, then the velocity of sound is :

Moderate

A

496 m/s
B

328 m/s
C

240 m/s
D

160 m/s

Solution

$Δn = n_{1} - n_{2} \Rightarrow 4 = \frac{v}{2 l_{1}} - \frac{v}{2 l_{2}} = \frac{v}{2} [\frac{1}{1 .00} - \frac{1}{1 .025}]$
$\Rightarrow 8 = v [1 - 0 .975] \Rightarrow V = \frac{8}{0 .025} \approx 328 m / s .$

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