Question

The frequency of transverse vibrations in a stretched string is 200Hz. If the tension is increased 4 times and the length is reduced to one fourth the original values, the frequency of vibrations will be:

• A. 25 Hz
• B. 200Hz
• C. 400Hz
• D. 1600Hz

Answer 1

The correct option is D 1600Hz

$f=\frac{\sqrt{T}}{L}$
so, $\frac{f_1}{f_2}=\frac{{}^{\sqrt{T_1}}{/}_{L_1}}{{}^{\sqrt{T_2}}{/}_{L_2}}$
$=\sqrt{\frac{T_1}{T_2}}\times \frac{L_2}{L_1}$
$=\sqrt{\frac{1}{4}}\times \frac{1}{4}$
$=\frac{1}{8}$
$\Rightarrow f_2=8\times f_1=8\times 200=1600Hz.$