Each of the two strings of length $51.6 \mathrm{~cm}$ and $49.1 \mathrm{~cm}$ are tensioned separately by…

Each of the two strings of length $51.6 \mathrm{~cm}$ and $49.1 \mathrm{~cm}$ are tensioned separately by $20 \mathrm{~N}$ force. Mass per unit length of both the strings is same and equal to $1 \mathrm{~g} / \mathrm{m}$. When both the strings vibrate simultaneously the number of beats is :
  1. 3
  2. 5
  3. 7
  4. 8

Solution

$\Delta v=\frac{\mathrm{V}}{2 \ell_1}-\frac{\mathrm{V}}{2 \ell_2}=\frac{\mathrm{V}}{2}\left[\frac{1}{\ell_1}-\frac{1}{\ell_2}\right]$ $=\frac{1}{2} \sqrt{\frac{\mathrm{T}}{\mu}}\left\{\frac{1}{\ell_1}-\frac{1}{\ell_2}\right\}$

Asked in: NEET 2009 (Mains)

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