The equation of a wave travelling in a string can be written as $y = 3\cos \pi (100t - x)$. Its wavelength is .... $cm$.

$A$ wave is represented by the equation $y = 0.5 \sin(10t - x) \ m$. It is a travelling wave propagating along the $+x$ direction with velocity .... $m/s$.

$A$ wave is represented by the equation: $y = a \sin(0.01x - 2t)$,where $a$ and $x$ are in $cm$. The velocity of propagation of the wave is .... $cm/s$.

For a wave equation $y = 10 \sin \pi (0.01x - 2.00t) \text{ cm}$,what is the maximum particle velocity in $\text{cm/sec}$?

State whether the following statements are True or False:
$(i)$ In the case of propagation of longitudinal waves,the angle between the directions of particle velocity and wave velocity is $0^{\circ}$ or $180^{\circ}$.
$(ii)$ In the case of propagation of transverse waves,the angle between the directions of particle velocity and wave velocity is $\pi \text{ rad}$.
$(iii)$ Along the direction of propagation of a wave,the distance between two particles having the same phase is called the wavelength of the wave.
$(iv)$ When a wave is reflected from a rarer medium,its phase increases by an amount of $\pi \text{ rad}$.

The displacement of a wave is given by $y=0.002 \sin (100t + x)$,where $x$ and $y$ are in meters and $t$ is in seconds. This represents a wave: