The displacement of a particle in a medium is $y = 10^{-4} \sin(100t + 20x + \frac{\pi}{3}) \ m$,where $t$ is in seconds and $x$ is in metres. The speed of the wave is (in $m/s$)

$A$ wave in a string has an amplitude of $2\, cm$. The wave travels in the $+ve$ direction of $x-$axis with a speed of $128\, m/s$ and it is noted that $5$ complete waves fit in $4\, m$ length of the string. The equation describing the wave is

Write the definition of wave speed and its $SI$ unit.

The displacement due to a wave moving in the positive $x$-direction is given by $y = \frac{1}{(1 + x^2)}$ at time $t = 0$ and by $y = \frac{1}{[1 + (x - 1)^2]}$ at $t = 2$ seconds,where $x$ and $y$ are in metres. The velocity of the wave in $m/s$ is

The equation of a travelling wave is $y = 60 \cos (1800t - 6x)$,where $y$ is in microns,$t$ is in seconds,and $x$ is in metres. The ratio of maximum particle velocity to the velocity of wave propagation is:

$A$ transverse wave is described by the equation $Y = Y_0 \sin 2\pi \left( ft - \frac{x}{\lambda} \right)$. The maximum particle velocity is four times the wave velocity if: