The equation of a plane progressive wave is given by $y = 0.025 \sin (100t + 0.25x)$. The frequency of this wave would be

$A$ wave is given by the equation $y=(0.02) \sin (\pi x - 8 \pi t)$. The velocity of the wave is (where $y$ and $x$ are in meters and $t$ is in seconds). (in $m/s$)

Which one of the following does not represent a travelling wave?

The equation of a wave is given by $y = 10 \sin \left( \frac{2 \pi}{45} t + \alpha \right)$. If the displacement is $5 \text{ cm}$ at $t = 0$,then the total phase at $t = 7.5 \text{ s}$ is

$A$ transverse wave is travelling along a string from left to right. The adjoining figure represents the shape of the string at a given instant. At this instant,among the following,choose the wrong statement.

Waves having a velocity $10 \text{ m/s}$ strike a stationary boat near the sea shore. The distance between two consecutive crests of the waves is $40 \text{ m}$. After how many seconds do the consecutive waves strike the boat (in $\text{ s}$)?