Question

If the length of a stretched string is shortened by $40\%$ and the tension is increased by $44\%$, then the ratio of the final and initial fundamental frequencies is:

• A. $2:1$
• B. $3:2$
• C. $3:4$
• D. $1:3$

Answer 1

The correct option is A $2:1$

length is shortened by $40\%$
$\Rightarrow length{l}_2=\frac{3l}{5}$
Tension is increased by $44\%$
$\Rightarrow$ Tension $T_2=\frac{144}{100}{T}_1$
$\therefore f=\frac{1}{2l}\sqrt{\frac{T}{\mu }}$
$\Rightarrow \frac{f_1}{f_2}=\frac{l_2}{l_1}\times \sqrt{\frac{T_2}{T_2}}$
$=\frac{3}{5}\times \frac{10}{12}$
$=\frac{1}{2}$
$\therefore$ final : initial$=2:1$