Question

A stretched string is in unison with a tuning fork of frequency 392Hz. If the length of the string is decreased by 2%, the number of beats heard per second is nearly

• A. 2
• B. 4
• C. 8
• D. 16

Answer 1

The correct option is C 8

Given : $\frac{l_1}{l_2}=\frac{100}{98}$

Frequency, $\left(f_1\right)=392H_z$

$\delta =\frac{v}{2l}$

$\frac{{\delta }_1}{{\delta }_2}=\frac{v/2l_1}{v/2l_2}$

$\frac{{\delta }_1}{{\delta }_2}=\frac{l_2}{l_1}=\frac{98}{100}$

${\delta }_2={\delta }_1\times \frac{100}{98}=392\times \frac{100}{98}=400H_z$

So, $beats={\delta }_2-{\delta }_1$ $=400-392$ $=8$