A wave represented by the given equation $y=a\cos (kx-\omega t)$ is superposed with another wave to form a stationary wave such that the point x = 0 is a node. The equation for the other wave is :

(1) $y=a\sin (kx+\omega t)$

(2) $y=-a\cos (kx+\omega t)$

(3) $y=-a\cos (kx-\omega t)$

(4) $y=-a\sin (kx-\omega t)$

A standing wave having 3 nodes and 2 antinodes is formed between two atoms having a distance 1.21 Å between them. The wavelength of the standing wave is :

(1) 1.21 Å

(2) 2.42 Å

(3) 6.05 Å

(4) 3.63 Å

In stationary waves, the distance between a node and its nearest antinode is 20 cm. The phase difference between two particles having a separation of 60 cm will be :

(1) Zero

(2) π/2

(3) π

(4) 3π/2

A standing wave is represented by $Y=A\sin \left(100t\right)\cos (0.01x)$ where Y and A are in millimetres, t is in seconds and x is in metres. The velocity of the wave is:

The stationary wave produced on a string is represented by the equation $y=5\cos (\pi x/3)\sin 40\pi t$ where x and y are in cm and t is in seconds. The distance between consecutive nodes is :

1. 5 cm

2. π cm

3. 3 cm

4. 40 cm

The tension in a piano wire is 10N. What should be the tension in the wire to produce a note of double the frequency :

(1) 5 N

(2) 20 N

(3) 40 N

(4) 80 N

Three similar wires of frequency n₁, n₂ and n₃ are joined to make one wire. Its frequency will be :

(1) $n=n_1+n_2+n_3$

(2) $\frac{1}{n}=\frac{1}{n_1}+\frac{1}{n_2}+\frac{1}{n_3}$

(3) $\frac{1}{\sqrt{n}}=\frac{1}{\sqrt{n_1}}+\frac{1}{\sqrt{n_2}}+\frac{1}{\sqrt{n_3}}$

(4) $\frac{1}{n^1}=\frac{1}{n_1^2}+\frac{1}{n_2^2}+\frac{1}{n_3^2}$

A string is rigidly tied at two ends and its equation of vibration is given by $y=\left(\cos 2\mathrm{\pi }t \right)\left(\sin 2\mathrm{\pi }x\right)$Then minimum length of the string is :

1. 1 m

2. $\frac{1}{2}m$

3. 5 m

4. 2π m

In an experiment with a sonometer, a tuning fork of frequency 256 Hz resonates with a length of 25 cm and another tuning fork resonates with a length of 16 cm. The tension of the string remaining constant the frequency of the second tuning fork is :

(1) 163.84 Hz

(2) 400 Hz

(3) 320 Hz

(4) 204.8 Hz

An empty vessel is getting filled with water, then the frequency of vibration of the air column in the vessel 

(1) Remains the same

(2) Decreases

(3) Increases

(4) First increases then decrease