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

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. $\frac{\mathrm{\pi }}{3}$