The percentage increase in the speed of transverse waves produced in a stretched string when the tension is increased by \(4\%\) is:
1. \(4\%\)
2. \(3\%\)
3. \(2\%\)
4. \(1\%\)

The mass per unit length of a uniform wire is \(0.135\) g/cm. A transverse wave of the form \(y=-0.21 \sin (x+30 t)\) is produced in it, where \(x\) is in meter and \(t\) is in second. The expected value of the tension in the wire is:

In an experiment with a sonometer, a tuning fork of frequency 256 Hz resonates with a length of 25 cm and another tuning fork resonates with a length of 16 cm. The tension of the string remaining constant the frequency of the second tuning fork is :

(1) 163.84 Hz

(2) 400 Hz

(3) 320 Hz

(4) 204.8 Hz

When a string is divided into three segments of lengths \(l_1,~l_2\text{ and }l_3,\) the fundamental frequencies of these three segments are \(\nu_1,~\nu_2\text{ and }\nu_3\) respectively. The original fundamental frequency \((\nu)\) of the string is:
1. \(\sqrt{\nu}=\sqrt{\nu_1}+\sqrt{\nu_2}+\sqrt{\nu_3}\)
2. \(\nu=\nu_1+\nu_2+\nu_3\)
3. \(\dfrac{1}{\nu}=\dfrac{1}{\nu_1}+\dfrac{1}{\nu_2}+\dfrac{1}{\nu_3}\)
4. \(\dfrac{1}{\sqrt{\nu}}=\dfrac{1}{\sqrt{\nu_1}}+\dfrac{1}{\sqrt{\nu_2}}+\dfrac{1}{\sqrt{\nu_3}}\)