The displacement equations of two waves are given as ${y_1} = 10\sin \left( {3\pi t + \frac{\pi }{3}} \right)$ and ${y_2} = 5(\sin 3\pi t + \sqrt 3 \cos 3\pi t)$. What is the ratio of their amplitudes?

$A$ traveling wave is described by the equation $y(x,t) = [0.05 \sin(8x - 4t)] \text{ m}$. The velocity of the wave is (All the quantities are in $SI$ units). (in $\text{ m/s}$)

What is the phase difference between two successive crests in a wave?

For the travelling harmonic wave $y(x, t) = 2.0 \cos 2 \pi(10 t - 0.0080 x + 0.35)$,where $x$ and $y$ are in $cm$ and $t$ is in $s$. Calculate the phase difference between oscillatory motion of two points separated by a distance of:
$(a)$ $4 \, m$
$(b)$ $0.5 \, m$
$(c)$ $\lambda / 2$
$(d)$ $3 \lambda / 4$

$A$ wave is represented by the equation $y = (0.02 \ m) \sin (5 \pi x - 20 t)$. The minimum distance between two particles always having the same speed is: (Assume $x$ and $t$ are in $SI$ units) (in $m$)

$A$ transverse wave of amplitude $0.5\, m$,wavelength $1\, m$,and frequency $2\, Hz$ is propagating in a string in the negative $x$-direction. The expression for this wave is: