Question

The speed of a wave on a string is $150m/s$ when the tension is $120$N. The percentage increase in the tension in order to raise the wave speed by $20\%$ is?

• A. $44\%$
• B. $40\%$
• C. $20\%$
• D. $10\%$

Answer 1

Answer: (A)

$44\%$

We know that $v=\sqrt{\frac{T}{m}}$
$v\propto \sqrt{T}$
$\frac{v_1}{v_2}=\sqrt{\frac{T_1}{T_2}}$
$\frac{T_1}{T_2}={\left(\frac{v_1}{v_2}\right)}^2$
$\frac{T_2-T_1}{T_1}=\frac{v_1^2-v_1^2}{v_1^2}$
$v_2=v_1+\frac{20}{100}{v}_1=\frac{120}{100}{v}_1=\frac{6}{5}{v}_1$
$=\frac{6}{5}\times 150$
$\frac{T_2-T_1}{T_1}=\frac{(180{)}^2-(150{)}^2}{(150{)}^2}$
$=\frac{30\times 330}{150\times 180}=0.47$
$=\frac{T_2-T_1}{T_1}\times 100=0.44\times 100=44\%$.