An observer on a sea-coast counts $45$ waves in one minute. If the wavelength of the waves is $7 \ m$,then the velocity of the waves will be (in $m/s$)

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:

$A$ travelling harmonic wave is represented by the equation $y(x, t) = 10^{-3} \sin(50t + 2x)$,where $x$ and $y$ are in meters and $t$ is in seconds. Which of the following is a correct statement about the wave?

$A$ boat at anchor is rocked by waves whose crests are $100 \ m$ apart and velocity is $25 \ m/s$. The boat bounces up once in every: ... $s$

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).

$A$ triangular pulse moving at $2 \ cm/s$ on a rope approaches an end at which it is free to slide on a vertical pole. What is the particle speed at the free end at $\frac{3}{4} \ s$ from the instant shown? (in $cm/s$)