First slide

Beats

Question

The length of two open organ pipes are $l$ and $l + Δ l (Δ l < < l)$ , if $u$ is the speed of sound, find the frequency of beats between them

Moderate

A

$\frac{v Δ l}{3 l^{2}}$
B

$\frac{v Δ l}{4 l^{2}}$
C

$\frac{v Δ l}{8 l^{2}}$
D

$\frac{v Δ l}{2 l^{2}}$

Solution

$B e a t f r e q u e n c y = f_{1} - f_{2} = \frac{v}{2 l} - \frac{v}{2 (l + Δ l)} = \frac{v}{2 l} [1 - {(1 + \frac{Δ l}{l})}^{- 1}] = \frac{v}{2 l} [1 - 1 + \frac{Δ l}{l}] = \frac{v Δ l}{2 l^{2}}$

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