First slide

Stationary waves

Question

The length of two open organ pipes are l and $(l + Δl)$ respectively. Neglecting end correction, the frequency of beats between them will be approximately
(Here v is the speed of sound)

Easy

A

$\frac{v}{2 l}$
B

$\frac{v}{4 l}$
C

$\frac{vΔl}{2 l^{2}}$
D

$\frac{vΔl}{l}$

Solution

$λ_{1} = 2 l, λ_{2} = 2 l + 2 Δl \Rightarrow n_{1} = \frac{v}{2 l} and n_{2} = \frac{v}{2 l + 2 Δl}$
$\Rightarrow$ No. of beats $= n_{1} - n_{2} = \frac{v}{2} (\frac{1}{l} - \frac{1}{l + Δl}) = \frac{vΔl}{2 l^{2}}$

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