Write the definition,unit,and dimensional formula of amplitude.

$A$ transverse wave given by $y=2 \sin (0.01 x+30 t)$ moves on a stretched string from one end to another end in $0.5 \ s$. If $x$ and $y$ are in $cm$ and $t$ is in $s$,then the length of the string is: (in $m$)

An observer on a sea-coast counts $45$ waves in one minute. If the wavelength of the waves is $7 \ m$,then the velocity of the waves will be (in $m/s$)

$A$ 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 $t = 20 \, s$.

In a plane progressive wave given by $y = 25 \cos (2\pi t - \pi x)$,the amplitude and frequency are respectively

$A$ wave is represented by the equation $y = 7\sin \{ \pi (2t - 2x) \} $ where $x$ is in metres and $t$ is in seconds. The velocity of the wave is ..... $m/s$.