In a medium, the phase difference between two particles separated by a distance $x$ is $\frac{\pi}{5} \text{ rad}$. If the frequency of the oscillation of particles is $25 \text{ Hz}$ and the velocity of propagation of the wave is $75 \text{ m/s}$, then the value of $x$ is (in $\text{ m}$)

$A$ transverse sinusoidal wave moves along a string in the positive $x$-direction at a speed of $10 \text{ cm/s}$. The wavelength of the wave is $0.5 \text{ m}$ and its amplitude is $10 \text{ cm}$. At a particular time $t$,the snapshot of the wave is shown in the figure. The velocity of point $P$ when its displacement is $5 \text{ cm}$ is:

$A$ wave is given by $y = 3 \sin 2\pi \left( \frac{t}{0.04} - \frac{x}{0.01} \right)$,where $y$ is in $cm$. The frequency of the wave and the maximum acceleration of the particle are:

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 metre and $t$ is in second. What is the phase difference between them?

$A$ wave travelling along the $x$-axis is described by the equation $y(x, t) = 0.005 \cos(\alpha x - \beta t)$. If the wavelength and the time period of the wave are $0.08 \ m$ and $2.0 \ s$,respectively,then $\alpha$ and $\beta$ in appropriate units are:

Write the definition of wave speed and its $SI$ unit.