For the wave $y(x, t) = 3.0 \sin (36 t + 0.018 x + \pi / 4)$,plot the displacement $(y)$ versus time $(t)$ graphs for $x = 0, 2$ and $4 \; cm$. What are the shapes of these graphs? In which aspects does the oscillatory motion in a travelling wave differ from one point to another: amplitude,frequency,or phase?

The relation between phase difference $(\Delta \phi)$ and path difference $(\Delta x)$ is:

The displacement $y$ of a wave travelling in the $x$-direction is given by $y = 10^{-4} \sin(600t - 2x + \frac{\pi}{3}) \, \text{m}$,where $x$ is expressed in metres and $t$ in seconds. The speed of the wave in $\text{m/s}$ is:

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.

$A$ wave travelling along the $x$-axis is described by the equation $y(x, t) = 0.005 \cos(\alpha x - \beta t)$. If the wavelength and the time period of the wave are $0.08 \ m$ and $2.0 \ s$,respectively,then $\alpha$ and $\beta$ in appropriate units are:

The transverse displacement $y(x, t)$ of a wave on a string is given by $y(x, t) = e^{-(ax^2 + bt^2 + 2\sqrt{ab}xt)}$. This represents: