Each of the two strings of length $51.6\,\, cm$ and $49.1\,\, cm$ are tensioned separately by $20\,\, N$ force. Mass per unit length of both the strings is same and equal to $1\,\, g/m.$ When both the strings vibrate simultaneously the number of beats is
AIPMT 2009, Medium
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$l_{1}=0.516 \mathrm{m}, l_{2}=0.491 \mathrm{m}, T=20 \mathrm{N}$
Mass per unit length, $\mu=0.001 \mathrm{kg} / \mathrm{m}$
Frequency, $v=\frac{1}{2 l} \sqrt{\frac{T}{\mu}}$
${v_{1}=\frac{1}{2 \times 0.516} \sqrt{\frac{20}{0.001}}}$
${v_{2}=\frac{1}{2 \times 0.491} \sqrt{\frac{20}{0.001}}}$
$\therefore \quad$ Number of beats $=v_{1}-v_{2}=7$
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