For a wave \(y=y_0 \sin (\omega t-k x)\), for what value of \(\lambda\) is the maximum particle velocity equal to two times the wave velocity?
1. \(\pi y_0\)
2. \(2\pi y_0\)
3. \(\pi y_0/2\)
4. \(4\pi y_0\)

If the equation of a wave is represented by:

$y$ $=$ ${10}^{-4}$ $\sin (100t$ $-$ $\frac{x}{10})m$, then the velocity of wave will be:
1.  100 m/s
2.  4 m/s
3.  1000 m/s
4.  0.00 m/s

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 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