For a wave \(y=y_0 \sin (\omega t-k x)\), for what value of \(\lambda\) is the maximum particle velocity equal to two times the wave velocity?
1. \(\pi y_0\)
2. \(2\pi y_0\)
3. \(\pi y_0/2\)
4. \(4\pi y_0\)

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

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

Two stationary sources exist, each emitting waves of wavelength λ. If an observer moves from one source to the other with velocity u, then the number of beats heard by him is equal to:

1. $\frac{2u}{\lambda }$

2. $\frac{u}{\lambda }$

3. $\sqrt{\mu \lambda }$

4. $\frac{\mu }{2\lambda }$

A string is cut into three parts, having fundamental frequencies n₁, n₂, and n₃ respectively. The original fundamental frequency "n" is related by the expression:

1. $\frac{1}{n}=\frac{1}{n_1}+\frac{1}{n_2}+\frac{1}{n_3}$

2. $n=n_1\times n_2\times n_3$

3. $n=n_1+n_2+n_3$

4. $n=\frac{n_1+n_2+n_3}{3}$

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)

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.  $\frac{n}{\sqrt{2}}$

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 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

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: