Mathematical Expression of a Wave

The differential equation of displacement of a wave is 

If $x-\alpha \sin \left(\omega t-\pi /6\right)$and $x=\alpha \cos \omega t$, then the phase difference between the two waves is 

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

The equation of a wave travelling on a string is $y=4\sin \left[\frac{\pi }{2}\left(8 \mathrm{t}-\frac{x}{8}\right)\right],$ where $x, y$ are in $\mathrm{cm}$ and $t$ in second. The velocity of the wave is

A wave is given by the equation, $y=A\sin \left[\pi \left(330t-x\right)\right]$, then frequency of the wave is

A plane wave is represented mathematically as

The velocity of a particle moving in the $x-y$ plane is given by $\frac{\mathrm{d}x}{\mathrm{d}t}=8\pi \sin 2\pi t$ and $\frac{\mathrm{d}y}{\mathrm{d}t}=-5\pi \cos 2\pi t$, where, $t=0, x=8$ and $y=0,$ then path of the particle is

The amplitude of a wave disturbance propagating in the positive x-direction is given by $\mathrm{y}=\frac{1}{1+{\mathrm{x}}^2}$ at $\mathrm{t}=0$ and $\mathrm{y}=\frac{1}{2+{\mathrm{x}}^2-2\mathrm{x}}$ at $\mathrm{t}=2\mathrm{s}$ , where x and y are in meter. Assuming that the shape of the wave disturbance does not change during the propagation, the speed of the wave is

The path difference between the two waves :

${\mathrm{y}}_1={\mathrm{a}}_1\sin \left(\omega \mathrm{t}-\frac{2\mathrm{\pi x}}{\mathrm{\lambda }}\right)$ and

${\mathrm{y}}_2={\mathrm{a}}_2\cos \left(\omega \mathrm{t}-\frac{2\mathrm{\pi x}}{\mathrm{\lambda }}+\mathrm{\varphi }\right)$ is

$y=3\sin \pi \left(\frac{1}{2}-\frac{x}{4}\right)$ represents an equation of a progressive wave, where $t$ is in $\mathrm{seconds}$ an $x$ is in $\mathrm{metre}$. The distance travelled by the wave in $5 \mathrm{s}$ is,

The equation of a wave is $3\cos \pi \left(50t-x\right)$. The wavelength of the wave is

The equation of a spherical progressive wave is

Which of the following functions represent a wave?

The transverse displacement $y\left(x,t\right)$ of a wave on a string is given by $y\left(x,t\right)=e^{-\left(a{x}^2+b{t}^2+2\sqrt{ab}xt\right)}$, this represents a

The equation of a progressive wave can be given by$y=15 \sin (660\pi t-0.02\pi x) \mathrm{cm}$. The frequency of the wave is

A wave equation is given by $y=4\sin \left[\pi \left(\frac{t}{5}-\frac{x}{9}+\frac{1}{6}\right)\right]$ where $x$ is in $\mathrm{cm}$ and $t$ is in second. Which of the following is true?

The equation of a wave is given as $y=0.07\sin \left(12\pi x-3000\pi t\right)$, where $x$ is in metre and $t$ in second, then the correct statement is

Equation of progressive wave is

$y=a\sin \left[10\pi x+11\pi t+\frac{\pi }{3}\right]$

The equation of a simple harmonic wave is given by $y=6\sin 2\pi (2t-0.1x)$, where $x$ and $y$ are in $\mathrm{mm}$ and $t$ is in second. The phase difference between two particles $2 \mathrm{mm}$ apart at any instant is

A plane progressive wave is given by y=2cos 6.284 (30t-x). What is period of the wave?