If the equation of a wave is represented by:

$y$ $=$ ${10}^{-4}$ $\sin (100t$ $-$ $\frac{x}{10})m$, then the velocity of wave will be:
1.  100 m/s
2.  4 m/s
3.  1000 m/s
4.  0.00 m/s

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. $\frac{\mathrm{\pi }}{3}$

If the tension and diameter of a sonometer wire of fundamental frequency n are doubled and density is halved, then its fundamental frequency will become:

1. $\frac{n}{4}$

2.  $\sqrt{2}$ $n$ $$

3.  n 

4.  $\frac{n}{\sqrt{2}}$

If a wave is travelling in a positive X-direction with A = 0.2 m, velocity = 360 m/s, and λ = 60 m, then the correct expression for the wave will be:

The phase difference between two waves, represented by
$\begin{array}{l}{\mathrm{y}}_1={10}^{-6}\sin \{100\mathrm{t}+(\mathrm{x}/50)+0.5\}\mathrm{m}\\ {\mathrm{y}}_2={10}^{-6}\cos \{100\mathrm{t}+\left(\frac{\mathrm{x}}{50}\right)\}\mathrm{m}\end{array}$
where X is expressed in metres and t is expressed in seconds, is approximate:
1. 2.07 radians
2. 0.5 radians
3. 1.5 radians
4. 1.07 radians

A cylindrical tube (L = 125 cm) is resonant with a tuning fork at a frequency of 330 Hz. If it is filled with water, then to get the resonance again, the minimum length of the water column will be: $(v_{air}$ $=$ $330$ $m/s)$
1.  50 cm
2.  60 cm
3.  25 cm
4.  20 cm

A point source emits sound equally in all directions in a non-absorbing medium. Two points, P and Q, are at distances of \(2\) m and \(3\) m, respectively, from the source. The ratio of the intensities of the waves at P and Q is:
1. \(3:2\)
2. \(2:3\)
3. \(9:4\)
4. \(4:9\)

If a standing wave having 3 nodes and 2 antinodes is formed within 1.21 Å distance, then the wavelength of the standing wave will be:
1. 1.21 Å
2. 2.42 Å
3. 0.605 Å
4. 4.84 Å

Two vibrating tuning forks produce progressive waves given by \(Y_1 = 4 ~\mathrm{sin}~500 \pi \mathrm{t}\) and \(Y_2 = 2 ~\mathrm{sin}~506 \pi \mathrm{t}\). The number of beats produced per minute is:

The equations of two waves are given as x = acos(ωt + δ) and y = a cos (ωt + $\alpha$), where δ = $\alpha$ + $\pi$/2, then the resultant wave can be represented by:

1. a circle (c.w)

2. a circle (a.c.w)

3. an ellipse (c.w)

4. an ellipse (a.c.w)