$A$ progressive sound wave is represented by $y = a \sin(400\pi t - \pi x / 6.85)$,where $x$ is in $m$ and $t$ is in $s$. The frequency of the wave is .... $Hz$.

The equation of a transverse wave travelling on a rope is given by $y = 10\sin \pi (0.01x - 2.00t)$ where $y$ and $x$ are in $cm$ and $t$ is in $seconds$. The maximum transverse speed of a particle in the rope is about .... $cm/s$.

Two waves are represented by the equations: $y_1 = a \sin(\omega t + kx + 0.57) \ m$ and $y_2 = a \cos(\omega t + kx) \ m$,where $x$ is in $meters$ and $t$ is in $seconds$. The phase difference between them is ..... $radian$.

Two waves of frequencies $20 Hz$ and $30 Hz$ travel out from a common point. The phase difference between them after $0.6 s$ is:

$A$ transverse wave is represented by $y = A \sin(\omega t - kx)$. For what value of the wavelength is the wave velocity equal to the maximum particle velocity?

The speed of a wave in a medium is $760\, m/s$. If $3600$ waves are passing through a point in the medium in $2$ minutes, then its wavelength is ...... $m$.