A tuning fork of frequency $392 Hz,$ resonates with $50 cm $ length of a string under tension ($T$). If length of the string is decreased by $2\%$, keeping the tension constant, the number of beats heard when the string and the tuning fork made to vibrate simultaneously is
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(c) $n \propto \frac{1}{l}$ ==> $\frac{{\Delta n}}{n} = - \frac{{\Delta l}}{l}$
If length is decreased by $2\%$ then frequency increases by $2\%$ i.e., $\frac{{{n_2} - {n_1}}}{{{n_1}}} = \frac{2}{{100}}$
==> ${n_2} - {n_1} = \frac{2}{{100}} \times {n_1} = \frac{2}{{100}} \times 392 = 7.8 \approx 8.$
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