$A$ plane progressive wave is given by $y = 2 \cos 2 \pi (330 t - x) \ m$. The frequency of the wave is: (in $Hz$)

$A$ 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

The equation of a longitudinal wave is represented as $y = 20 \cos \pi (50t - x)$. Its wavelength is ..... $cm$.

For a transverse wave travelling along a straight line,the distance between two peaks (crests) is $5 \, m$,while the distance between one crest and one trough is $1.5 \, m$. The possible wavelengths (in $m$) of the waves are

$A$ 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 ..... $m/s$.

The equation of a progressive wave is given by $y = 6 \cos(100t - 4x)$ where $y$ is in $\mu\text{m}$, $x$ is in metre and $t$ is in second. The ratio of the maximum particle velocity to the velocity of wave is