Two waves represented by the following equations are travelling in the same medium \(y_1 = 5\sin2\pi(75t-0.25x), y_2= 10\sin\pi(150t-0.50 x)\). The intensity ratio \(\dfrac{I_1}{I_2}\) of the two waves is:
1. \(1:2\)
2. \(1:4\)
3. \(1:8\)
4. \(1:16\)

Two tuning forks when sounded together produced 4 beats/sec. The frequency of one fork is 256 Hz. The number of beats heard increases when the fork of frequency 256 Hz is loaded with wax. The frequency of the other fork is(in Hz) :

(1) 504

(2) 520

(3) 260

(4) 252

Beats are produced by two waves given by $y_1=a\sin 2000\pi t$ and $y_2=a\sin 2008\pi t$. The number of beats heard per second is :

(1) Zero

(2) One

(3) Four

(4) Eight

The distance between the nearest node and antinode in a stationary wave is :

(1) λ

(2) $\frac{\lambda }{2}$

(3) $\frac{\lambda }{4}$

(4) 2λ

For the stationary wave $y=4\sin \left(\frac{{\displaystyle \pi x}}{{\displaystyle 15}}\right)\cos \left(96\pi t\right)$, the distance between a node and the next antinode is :

1. 7.5

2. 15

3. 22.5

4. 30

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 is represented by

$Y=A\sin \left(100t\right)\cos (0.01x)$

where Y and A are in millimetre, t is in seconds and x is in metre. The velocity of the wave is :

(1) 10⁴ m/s

(2) 1 m/s

(3) 10^–4 m/s

(4) Not derivable from the above data