The equation of the sinusoidal wave is given by $y\left(x,t\right)=\left(30\mathrm{m}\right) \sin \left(5\mathrm{\pi x}-16\mathrm{\pi }t\right)$. The amplitude of the sinusoidal wave is in meter.

The transverse displacement at position $x$ and time $t$ in a string due to a travelling wave is given by $y(x, t)=$$3.0\cos (\pi x-4\pi t)\mathrm{cm}$, where $x$ is in centimeters and $t$ is in seconds. Which of the following statements is wrong?

A uniform string of length $20 \mathrm{m}$ is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the support is 

(Take, $\mathrm{g}=10\mathrm{ }\mathrm{m} {\mathrm{s}}^{-2}$)

A transverse wave propagating along $x$ -axis is represented by

$y\left(x,t\right)=8.0\sin \left(0.5\pi x-4\pi t-\frac{\pi }{4}\right)$

where $x$ is in meters and $t$ is in seconds. The speed of the wave is

The propagation constant or angular wave number is $\underline{ }$