The displacement of a particle is given by \(y = 5\times 10^{-4}\sin\left(100t-50x\right),\) where \(x\) is in metres and \(t\) is in seconds. The velocity of the wave is:
1. \(5000~\text{m/s}\)
2. \(2~\text{m/s}\)
3. \(0.5~\text{m/s}\)
4. \(300~\text{m/s}\)

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. $y=f(x^2-v{t}^2)$

A transverse wave is represented by the equation $y=y_0\sin \frac{2\pi }{\lambda }(vt-x)$

For what value of λ, the maximum particle velocity equal to two times the wave velocity?

(1) $\lambda =2\pi y_0$

(2) $\lambda =\pi y_0/3$

(3) $\lambda =\pi y_0/2$

(4) $\lambda =\pi y_0$

A wave travels in a medium according to the equation of displacement given by $y(x,t)=0.03\sin \pi (2t-0.01x)$ where y and x are in metres and t in seconds. The wavelength of the wave is :

1. 200 m

2. 100 m

3. 20 m

4. 10 m

The frequency of the sinusoidal wave $y=0.40\cos [2000t+0.80x]$ would be :

(1) 1000 π Hz

(2) 2000 Hz

(3) 20 Hz

(4) $\frac{1000}{\pi }Hz$

The equation of a plane progressive wave is given by $y=0.025\sin (100t+0.25x)$. The frequency of this wave would be :

(1) $\frac{50}{\pi }Hz$

(2) $\frac{100}{\pi }Hz$

(3) 100 Hz

(4) 50 Hz

In the given progressive wave equation, what is the maximum velocity of particle $Y=0.5\sin (10\pi t-5x)$cm 

(1) 5 cm/s

(2) 5π cm/s

(3) 10 cm/s

(4) 10.5 cm/s

Two waves of frequencies 20 Hz and 30 Hz travel out from a common point. The phase difference between them after 0.6 sec is :

(1) Zero

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

(3) π

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