What is the phase difference between two successive crests in a wave?

The path difference between two waves $Y_1 = a_1 \sin \left(\omega t - \frac{2 \pi x}{\lambda}\right)$ and $Y_2 = a_2 \cos \left(\omega t - \frac{2 \pi x}{\lambda} + \phi\right)$ is

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

The figure represents the instantaneous picture of a longitudinal harmonic wave travelling along the negative $x$-axis. Identify the correct statement$(s)$ related to the movement of the points shown in the figure. The points with maximum displacement are:

The equation of a wave is given by $Y = 10^{-2} \sin 2 \pi (160 t - 0.5 x + \frac{\pi}{4})$,where $x$ and $Y$ are in $m$ and $t$ is in $s$. The speed of the wave is $..... \, km \, h^{-1}$.

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