In a wave motion $y = a \sin (kx - \omega t)$,$y$ can represent

$A$ wave is given by $y=5 \times 10^{-3} \sin \left(12.5 \pi x - \frac{\pi}{2} t\right)$. Then its wavelength and time period are respectively ($y$ and $x$ are in metres and $t$ is in seconds).

The figure shows a sinusoidal wave at a given instant. Which points are in the same phase?

Which of the following functions for $y$ can never represent a travelling wave?

One end of a long string of linear mass density $8.0 \times 10^{-3} \; kg \; m^{-1}$ is connected to an electrically driven tuning fork of frequency $256 \; Hz$. The other end passes over a pulley and is tied to a pan containing a mass of $90 \; kg$. The pulley end absorbs all the incoming energy so that reflected waves at this end have negligible amplitude. At $t=0$,the left end (fork end) of the string $x=0$ has zero transverse displacement $(y=0)$ and is moving along the positive $y$-direction. The amplitude of the wave is $5.0 \; cm$. Write down the transverse displacement $y$ as a function of $x$ and $t$ that describes the wave on the string.

Two waves are represented by the equations $y_1 = A \sin (\omega t + kx + 0.57) \ m$ and $y_2 = A \cos (\omega t + kx) \ m$,where $x$ is in metre and $t$ is in second. What is the phase difference between them?