$A$ wave is represented by $x = 0.4 \cos \left(8t - \frac{y}{2}\right)$ where $x$ and $y$ are in meters and $t$ is in seconds. The speed of the wave is

In the given progressive wave $y = 5 \sin(100\pi t + 0.4\pi x)$,where $y$ and $x$ are in $m$ and $t$ is in $s$. Find the:
$(a)$ Amplitude
$(b)$ Wavelength
$(c)$ Frequency
$(d)$ Wave velocity
$(e)$ Particle velocity amplitude.

The diagram below shows an instantaneous position of a string as a transverse progressive wave travels along it from left to right. Which one of the following correctly shows the direction of the velocity of the points $1, 2$ and $3$ on the string?

The equation of a progressive wave is $y = 0.2 \sin 2\pi \left[ \frac{t}{0.01} - \frac{x}{0.3} \right]$,where $x$ and $y$ are in meters and $t$ is in seconds. The velocity of propagation of the wave is .... $m/s$.

$A$ plane progressive wave propagating along the positive $x$-axis is represented by:

Given below are some functions of $x$ and $t$ to represent the displacement (transverse or longitudinal) of an elastic wave. State which of these represent a travelling wave.