$A$ transverse harmonic wave on a string is given by $y(x, t) = 5 \sin (6t + 0.003x)$,where $x$ and $y$ are in $cm$ and $t$ is in $s$. The wave velocity is $...........\,ms^{-1}$.

$A$ transverse wave propagates in a medium with a velocity of $1450 \, m/s$. The distance between the nearest points at which the oscillations of the particles are in the opposite phase (phase difference of $\pi$) is $0.1 \, m$. What is the frequency of the wave in $Hz$?

Which one of the following does not represent a travelling wave?

The equation of a simple harmonic progressive wave is given by $Y = a \sin 2 \pi (b t - c x)$. The maximum particle velocity will be twice the wave velocity if:

$Assertion :$ Speed of wave $= \frac{\text{wavelength}}{\text{time period}}$
$Reason :$ Wavelength is the distance between two nearest particles in phase.

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