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:

1.	\(12.15\) N	2.	\(30.12\) N
3.	\(45.35\) N	4.	\(50.24\) N

Which, of the following equation represents a travelling wave?
1. \(y=A\sin(15x-2t)\)
2. \(y=Ae^{-x^2}(vt+\theta)\)
3. \(y=Ae^{x}\cos (\omega t-\theta)\)
4. \(y=A\sin x \cos \omega t\)

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. \(1\%\)

A string of length \(2.0~\text{m},\) fixed at both ends is driven by a \(240~\text{Hz}\) vibrator. If the string vibrates in its third harmonic mode, the speed of the wave and its fundamental frequency, respectively, are:

Two waves have the following equations:

$x_1$ $=$ $a$ $\sin$ $(\omega t$ $+$ ${\varphi }_1)$
$x_2$ $=$ $a$ $\sin$ $(\omega t$ $+$ ${\varphi }_2)$

If in the resultant wave, the frequency and amplitude remain equal to the amplitude of superimposing waves, then the phase difference between them will be:

1.  $\frac{\mathrm{\pi }}{6}$

2. $\frac{2\mathrm{\pi }}{3}$

3. $\frac{\mathrm{\pi }}{4}$

4. $\frac{\mathrm{\pi }}{3}$

Two waves are represented by; \(y=a\text{sin}(\omega t-kx)\) and \(y=a\text{cos}(\omega t-kx)\) are superposed. The resultant wave will have an amplitude:
1. \(a\)
2. \(\sqrt{2} a\)
3. \(2a\)
4. \(0\)

Two sine waves travel in the same direction in a medium. The amplitude of each wave is \(A\) and the phase difference between the two waves is \(120^\circ.\) The resultant amplitude will be:
1. \(A\)
2. \(2A\)
3. \(4A\)
4. \(\sqrt2 A\)

A transverse wave travels along the Z-axis. The particles of the medium must move: