Which one of the following statements is true?

The displacement of a particle is given by $y=5\times {10}^{-4}\sin (100t-50x)$, where x is in metres and t is in seconds. The velocity of the wave is:

1. 5000 m/sec

2. 2 m/sec

3. 0.5 m/sec

4. 300 m/sec

If a wave is travelling in a positive X-direction with A = 0.2 m, velocity = 360 m/s, and λ = 60 m, then the correct expression for the wave will be:

A wave traveling in the +ve \(x\)-direction having maximum displacement along \(y\)-direction as \(1~\text{m}\), wavelength \(2\pi ~\text{m}\) and frequency of \(\frac{1}{\pi}~\text{Hz}\), is represented by:
1. \(y=\sin (2 \pi x-2 \pi t)\)
2. \(y=\sin (10 \pi x-20 \pi t)\)
3. \(y=\sin (2 \pi x+2 \pi t)\)
4. \( y=\sin (x-2 t)\)

The equation \(y(x,t) = 0.005 ~cos (\alpha x- \beta t)\) describes a wave traveling along the x-axis. If the wavelength and the time period of the wave are 0.08 m and 2.0 s, respectively, then $\mathrm{\alpha }$ and $\mathrm{\beta }$ in appropriate units are:

1. $\mathrm{\alpha }=25.00$ $\mathrm{\pi },$ $\mathrm{\beta }=\mathrm{\pi }$

2. $\mathrm{\alpha }=\frac{0.08}{\mathrm{\pi }},$ $\mathrm{\beta }=\frac{2.0}{\mathrm{\pi }}$

3. $\mathrm{\alpha }=\frac{0.04}{\mathrm{\pi }},$ $\mathrm{\beta }=\frac{1.0}{\mathrm{\pi }}$

4. $\mathrm{\alpha }=12.50$ $\mathrm{\pi },$ $\mathrm{\beta }=\frac{\mathrm{\pi }}{2.0}$

The equation of a progressive wave is given by $y=4\sin \left\{\pi \left(\frac{{\displaystyle t}}{{\displaystyle 5}}-\frac{{\displaystyle x}}{{\displaystyle 9}}\right)+\frac{{\displaystyle \pi }}{{\displaystyle 6}}\right\}$.
Which of the following is correct​​​​?
1. v = 5 m / sec
2.  λ = 18 m
3.  a = 0.04 m
4.  n = 50 Hz

If a travelling wave pulse is given by \(y=\frac{20}{4+(x+4 t)^2}~\text{m}\), then:

A transverse wave is represented by y = Asin(ωt -kx). At what value of the wavelength is the wave velocity equal to the maximum particle velocity?

1. $\pi$A/2

2. $\pi$A

3. 2$\pi$A

4. A

Given the equation for a wave on the string, y = 0.5 sin(5x - 3t) where y and x are in metres and t in seconds, the ratio of the maximum speed of particle to the speed of wave is:

1. 1:1

2. 5:2

3. 3:2

4. 4:5

The wave described by y=0.25 sin(10$\pi x-2\pi t$), where x and y are in metres and t in seconds, is a wave traveling along the: