Two closed organ pipes, when sounded simultaneously gave 4 beats … - Vidyadip

MCQ

Two closed organ pipes, when sounded simultaneously gave 4 beats per sec. If longer pipe has a length of $1 \mathrm{~m}$. Then length of shorter pipe will be, $(v=300 \mathrm{~m} / \mathrm{s})$

A
$185.5 \mathrm{~cm}$
✓
$94.9 \mathrm{~cm}$
C
$90 \mathrm{~cm}$
D
$80 \mathrm{~cm}$

✓

Answer

Correct option: B.

$94.9 \mathrm{~cm}$

(b) For first pipe $n_1=\frac{v}{4 l_1}$ and for second pipe $n_2=\frac{v}{4 l_2}$
So, number of beats $=n_2-n_1=4$
$\Rightarrow 4=\frac{v}{4}\left(\frac{1}{l_2}-\frac{1}{l_1}\right) $
$\Rightarrow 16=300(\frac{1}{l_2}-\frac{1}{1})$
$\Rightarrow l_2=94.9\mathrm{~cm}$

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