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:

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

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

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:

Two progressive waves are represented by, \(y_1=5sin(200t-3.14x)\) and
 \(y_2=10sin(200t-3.14x+\frac{\pi}{3})\) (\(x\) is in metres, and \(t\) is in seconds). Path difference between the two waves is:
1. $\frac{100}{\mathrm{\pi }}\mathrm{ m}$

2. $\frac{1}{3}\mathrm{ m}$

3. $3.14\times \frac{\mathrm{\pi }}{3}\mathrm{ m}$

4. $\frac{{\mathrm{\pi }}^2}{9}\mathrm{ m}$

The phase difference between two waves, represented by
$\begin{array}{l}{\mathrm{y}}_1={10}^{-6}\sin \{100\mathrm{t}+(\mathrm{x}/50)+0.5\}\mathrm{m}\\ {\mathrm{y}}_2={10}^{-6}\cos \{100\mathrm{t}+\left(\frac{\mathrm{x}}{50}\right)\}\mathrm{m}\end{array}$
where X is expressed in metres and t is expressed in seconds, is approximate:
1. 2.07 radians
2. 0.5 radians
3. 1.5 radians
4. 1.07 radians

The mathematical forms for three sinusoidal traveling waves are given by: 
Wave 1 : y(x,t) = (2cm) sin(3x–6t)
Wave 2 : y(x,t) = (3cm) sin(4x–12t)
Wave 3 : y(x,t) = (4cm) sin(5x–11t)
where x is in meters and t is in seconds. Of these waves :