Q122 / 160 · AP EAMCET 2012 · Physics

When a vibrating tuning fork is placed on a sound box of a sonometer, 8 beats per second are heard when the length of the sonometer wire is kept at $101 \mathrm{~cm}$ or $100 \mathrm{~cm}$. Then the frequency of the tuning fork is (Consider that the tension in the wire is kept constant)

  • A
    $1616 \mathrm{~Hz}$
  • Correct answer
    B
    $1608 \mathrm{~Hz}$
  • C
    $1632 \mathrm{~Hz}$
  • D
    $1600 \mathrm{~Hz}$

Solution

We have, $n l=$ constant $\begin{aligned} n_1 l_1 & =n_2 l_2 \\ (n+8) 100 & =(n-8) 101 \\ \frac{n+8}{n-8} & =\frac{101}{100} \\ \frac{n}{8} & =\frac{201}{1} \\ n & =1608\end{aligned}$

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

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