A transverse harmonic wave on a string is described by, \(y(x,t) = 3.0 ~\sin ( 36t + 0.018x + {\dfrac {\pi} 4})\) where \(x\) and \(y\) are in cm and \(t\) in sec. The positive direction of \(x\) is from left to right. What is the shortest distance between two successive crests in the wave?

For the travelling harmonic wave, \(y(x,t) = 2.0\ \text{cos}\ 2\pi (10t - 0.0080x + 0.35 )\) where \(x\) and \(y\) are in \(\text{cm}\) and \(t\) is in seconds. The phase difference between the oscillatory motion of two points separated by a distance of \(4~\text{m}\) will be:
1. \(0.8 \pi\ \text{rad}\)
2.  \(\pi\ \text{rad}\)
3. \(6.4\pi\ \text{rad}\)
4. \(4\pi\ \text{rad}\)