It is possible to hear beats from the two vibrating sources of frequency :

(1) 100 Hz and 150 Hz

(2) 20 Hz and 25 Hz

(3) 400 Hz and 500 Hz

(4) 1000 Hz and 1500 Hz

Two vibrating tuning forks produce progressive waves given by $Y_1=4\sin 500\pi t$ and $Y_2=2\sin 506\pi t.$ Number of beats produced per minute is :

(1) 360

(2) 180

(3) 3

(4) 60

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

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