When a string is divided into three segments of lengths \(l_1\), \(l_2\) and \(l_3\), the fundamental frequencies of these three segments are \(\nu_1\), \(\nu_2\) 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.	\(\dfrac{1}{\sqrt{\nu}} =\dfrac{1}{\sqrt{\nu_1}} +\dfrac{1}{\sqrt{\nu_2}}+\dfrac{1}{\sqrt{\nu_3}}\)

A transverse wave is represented by \(y=A\mathrm{sin}(\omega t-kx).\) At what value of the wavelength is the wave velocity equal to the maximum particle velocity?
1. \(\pi A/2\)
2. \(\pi A\)
3. \(2\pi A\)
4. \(A\)

The wave described by \(y=0.25\sin (10\pi x-2\pi t)\), where \(x \) and \(y\) are in metre and \(t\) in second, is a wave travelling along the:

Which one of the following does not represent a travelling wave?

1. $y=\sin (x-vt)$

2. $y=y_m\sin k(x+vt)$

3. $y=y_m\sin (x-vt)$

4. $y=f(x^2-v{t}^2)$

Two points are located at a distance of \(10\) m and \(15\) m from the source of oscillation. The period of oscillation is \(0.05\) s and the velocity of the wave is \(300\) m/s. What is the phase difference between the oscillations of two points?
1. \(\pi/3\)
2. \(2\pi/3\)
3. \(\pi\)
4. \(\pi/6\)

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. \(\dfrac{1}{\sqrt{\nu}}=\dfrac{1}{\sqrt{\nu_1}}+\dfrac{1}{\sqrt{\nu_2}}+\dfrac{1}{\sqrt{\nu_3}}\)

A wave travelling in the positive \(x\)-direction having maximum displacement along \(y\)-direction as \(1~\text{m},\) wavelength \(2\pi~\text{m}\) and frequency of \(1/ \pi\) Hz is represented by:
1. \(y=\text{sin}(x-2t)\)
2. \(y=\text{sin}(2\pi x-2\pi t)\)
3. \(y=\text{sin}(10\pi x-20\pi t)\)
4. \(y=\text{sin}(2\pi x+2\pi t)\)

Which of the following is not possible for sound waves in air?
1. beats
2. interference
3. diffraction
4. polarization