The equation of a progressive wave is given by $x = 0.05 \cos \left( 4\pi t + \frac{\pi}{4} \right) \, m$. What is the frequency of the wave in $Hz$?

The figure represents the instantaneous snapshot of a transverse harmonic wave traveling along the negative $x$-axis. Identify the correct point(s) moving in the negative $y$-direction (downward).

$A$ transverse wave given by $y=2 \sin (0.01 x+30 t)$ moves on a stretched string from one end to another end in $0.5 \ s$. If $x$ and $y$ are in $cm$ and $t$ is in $s$,then the length of the string is: (in $m$)

$A$ sound wave of frequency $245 \,Hz$ travels with the speed of $300 \,ms^{-1}$ along the positive $x$-axis. Each point of the wave moves to and fro through a total distance of $6 \,cm$. What will be the mathematical expression of this travelling wave?

Two waves are represented by the equations $y_1 = a \sin \omega t$ and $y_2 = a \cos \omega t$. The first wave is .....

When a sound wave of wavelength $\lambda$ is propagating in a medium, the maximum velocity of the particle is equal to the wave velocity. The amplitude of the wave is: