$A$ simple wave motion is represented by $y=5(\sin 4 \pi t+\sqrt{3} \cos 4 \pi t)$. Its amplitude is

$A$ person is producing a wave in a string by moving his hand first up and then down. If the frequency is $\frac{1}{8} \, Hz$,then find out the time taken by a particle which is at a distance of $9 \, m$ from the source to move to the lower extreme for the first time in seconds. (Given $\lambda = 24 \, m$)

What is the phase change of a wave when it reflects from a rigid support?

$A$ plane progressive wave is given by $y = 2 \cos 6.284(330t - x)$. What is the period of the wave?

$A$ transverse wave on a string is described by $y = 3 \sin(36t + 0.018x + \pi/4)$,where $x$ and $y$ are in $cm$ and $t$ is in seconds. The least distance between two successive crests in the wave is . . . . . . $cm$. (Nearest integer) $(\pi = 3.14)$

$A$ travelling acoustic wave of frequency $500 Hz$ is moving along the positive $x$-direction with a velocity of $300 ms^{-1}$. The phase difference between two points $x_{1}$ and $x_{2}$ is $60^{\circ}$. The minimum separation between the two points is: