When a stretched wire and a tuning fork are sounded together, 5 beats per second are produced, when length of wire is $95 \mathrm{~cm}$ or $100 \mathrm{~cm}$, frequency of the fork is

• A

  $90 \mathrm{~Hz}$
• B

  $100 \mathrm{~Hz}$
• C

  $105 \mathrm{~Hz}$
• Correct answer
  D

  $195 \mathrm{~Hz}$

Solution

Let the frequency of tuning fork be $n$. Suppose $l_1=95 \mathrm{~cm}$ has frequency $n_1$ and $l_2=100 \mathrm{~cm}$ has frequency $n_2\left( < n_1\right)$
Also, $\quad \frac{n_1}{n_2}=\frac{l_2}{l_1}=\frac{100}{95}$ $n_1=\frac{100}{95} n_2$ From eqn. (iii), $\frac{100}{95} n_2-n_2=10, n_2=190$ From eqn. (ii), $n=n_2+5=190+5=195 \mathrm{~Hz}$.

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