Question

The tension in a wire is decreased by $19\%$ The percentage decrease in frequency will be

• A. $0.19\%$
• B. $10\%$
• C. $19\%$
• D. $0.9\%$

Answer 1

Answer: (B)

$10\%$

GIven,

$T_1=100$$

$T_2=100-19=81$%

The frequency is proportional to the square root of tension.

$f\propto \sqrt{T}$

$\frac{f_1}{f_2}=\sqrt{\frac{T_1}{T_2}}$

$\frac{f_1}{f_2}=\sqrt{\frac{100}{81}}=\frac{10}{9}$

The percentage change in frequency will be

$=1-\frac{f_2}{f_1}\times 100$$

$=1-\frac{9}{10}\times 100=\frac{1}{10}\times 100$

$=10$%

The correct option is B.