$A$ wave equation which gives the displacement along $y$-direction is given by $y = 0.001 \sin(100t + x)$,where $x$ and $y$ are in meters and $t$ is time in seconds. This represents a wave:

Explain the amplitude and phase of a wave.

$A$ small amplitude progressive wave in a stretched string has a speed of $100 \ cm/s$ and a frequency of $100 \ Hz$. The phase difference between two points $2.75 \ cm$ apart on the string,in radians,is

In the wave equation $y = 0.5 \sin \frac{2 \pi}{\lambda}(400 t - x ) \, m$,the velocity of the wave will be ......... $m/s$.

The phase difference between two waves represented by $y_1 = 10^{-6} \sin [100t + (x/50) + 0.5] \, m$ and $y_2 = 10^{-6} \cos [100t + (x/50)] \, m$,where $x$ is expressed in meters and $t$ is expressed in seconds,is approximately .... $rad$.

$A$ wave travelling along a string is described by,
$y(x, t) = 0.005 \sin (80.0 x - 3.0 t)$
In which the numerical constants are in $SI$ units ($0.005 \, m, 80.0 \, rad \, m^{-1},$ and $3.0 \, rad \, s^{-1}$). Calculate
$(a)$ the amplitude,
$(b)$ the wavelength,and
$(c)$ the period and frequency of the wave.
Also,calculate the displacement $y$ of the wave at a distance $x = 30.0 \, cm$ and time $t = 20 \, s$.