Q116 / 197 · NEET 2009 (Mains) · Physics

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 :

  • A
    3
  • B
    5
  • Correct answer
    C
    7
  • D
    8

Solution

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

Hence, the correct answer is option: 'C'.

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