Question

The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by $4\%$ will be$\_\_\_\%$.

Answer 1

Step 1: Given data:

The tension is increased by $4\%$

Step 2: Formula used:

Speed of transverse wave is $V=\sqrt{\frac{T}{\mu }}$

Where $\mu$is mass per unit length

$T$ is the tension of the string.

Step 3: Calculating the percentage increase in the speed of transverse waves produced in a stretched string:

Using the formula of the speed of a transverse wave-

$V=\sqrt{\frac{T}{\mu }}$

Taking relative change-

$\begin{array}{rcl}\left(\frac{\Delta v}{v}\right)& =& \left(\frac{1}{2}\right)\frac{\Delta T}{T}\\ \left(\frac{\Delta v}{v}\right)\times 100& =& \frac{1}{2}\hspace{0.17em}\left(\frac{\hspace{0.17em}\Delta T}{T}\right)\times 100\\ & =& \frac{1}{2}\times 4\left[\mu iscons\tan tforastring\right]\\ & =& 2\%\end{array}$

Thus, The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by $4\%$ will be $2\%$