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Q.

Two open pipes oi length I are vibrating simultaneously. If length of one of the pipes is reduced by y, then the number of beats heard per second will be
(if the velocity of sound is v and y < /)

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a

$\frac{Vy}{2 l^{2}}$

b

$\frac{v^{2} y}{2 l^{2}}$

c

$\frac{{Vy}^{2}}{2 l}$

d

$\frac{V^{2} y^{2}}{2 l}$

answer is A.

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Detailed Solution

for an open pipe, $n = \frac{V}{2 l}$
$n_{1} = \frac{V}{2 (l â y)} and n_{2} = \frac{V}{2 l} oR În = \frac{V}{2 (l â y)} â \frac{V}{2 l} = \frac{V}{2} [\frac{1}{(l â y)} â \frac{1}{l}] = \frac{V}{2} [\frac{l â (l â y)}{l (l â y)}] = \frac{Vy}{2 l (l â y)} = \frac{Vy}{2 l^{2}} (âµ l >> y)$

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