Wave Equation Questions

The wave described by $y=0.25\sin (10\pi x-2\pi t)$, where $x$ and $y$ are in meters and $t$ in seconds, is a wave travelling along the:

A wave in a string has an amplitude of $2\text{cm}$. The wave travels in the $+ve$ direction of $x$ axis with a speed of $128\text{m/sec}$ and it is noted that $5$ complete waves fit in $4\text{m}$ length of the string. The equation describing the wave is:

The equation of a simple harmonic wave is given by $y=3\sin \frac{\pi }{2}(50t-x)$. The ratio of maximum particle velocity to the wave velocity is:

A wave travelling in the $+x$ direction having displacement along $y$ as $1\text{m}$, wavelength $2\pi \text{m}$ and frequency $\frac{1}{\pi }\text{Hz}$ is represented by: