Equation of a progressive wave is given by

$y=0.2\cos \left(0.04\pi t+0.02\pi x-\frac{{\displaystyle \pi }}{{\displaystyle 6}}\right)$

The distance is expressed in cm and time in second. What will be the minimum distance between two particles having the phase difference of π/2 :

1. 4 cm

2. 8 cm

3. 25 cm

4. 12.5 cm

Which one of the following does not represent a traveling wave :

1. $y=\sin (x-vt)$

2. $y=y_m\sin k(x+vt)$

3. $y=y_m\sin (x-vt)$

4. $y=f(x^2-v{t}^2)$

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