The equation of a progressive wave is given by $y = 0.5 \sin(10t + x) \text{ m}$. What is the wave velocity in $\text{m/s}$?

The figure shows four progressive waves $A, B, C$ and $D$ with their phases expressed with respect to the wave $A$. It can be concluded from the figure that

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 shows the propagation of a progressive wave. $A$,$B$,$C$,$D$,$E$,and $F$ are points on this wave. Which of the following points are in the same state of vibration (i.e.,in the same phase)?

$y=3 \sin \pi\left(\frac{t}{2}-\frac{x}{4}\right)$ represents an equation of a progressive wave,where $t$ is in $s$ and $x$ is in $m$. The distance travelled by the wave in $5 \,s$ is (in $\,m$)

Among the following,the equation representing a progressive wave is
$(A)$ $y=2 \cos 3x \sin 10t$
$(B)$ $y=2 \sqrt{x-vt}$
$(C)$ $y=3 \sin (5x-0.5t)+4 \cos (5x-0.5t)$
$(D)$ $y=\cos x \sin t+\cos 2x \sin 2t$