A sine wave is travelling in a medium. The minimum distance between two particles always having same speed is $(\lambda$ is the wavelength of wave)

A travelling wave passes through a point of observation. At this point, the time interval between successive crests is $0.2 \mathrm{s}$, then,

When a wave travels in a medium, displacement of a particle is given by, $y(x,t)=0.03\sin \pi (2t-0.01x)$, where $y$ and $x$ are in metres and $t$ in seconds. The phase difference at a given instant of time between two particles $25 \mathrm{m}$ apart in the medium is

If the wave equation of a particle is represented by, $y=0.8\sin \left(20\pi t-5\pi x+\frac{\pi }{4}\right)$, where $x$ and $y$ are measured in metre and $t$ is measured in seconds, then the wave equation represents a wave travelling in

A transverse wave of amplitude $0.5 \mathrm{m}$, wavelength $1 \mathrm{m}$ and frequency $2 \mathrm{Hz}$ is propagating in a string in the negative$x$-direction. The equation of this wave is

The equation of a wave is $y=4\sin \left\{\frac{\pi }{2}\left(2t+\frac{x}{8}\right)\right\}$ where $y, x$ are in $\mathrm{cm}$ and time is in second. The amplitude, wavelength, velocity and frequency of the wave are respectively

The equation of a wave is $y=4$$\sin \left\{\frac{\pi }{2}\left(2t+\frac{x}{8}\right)\right\}$, where $y, x$ are in $\mathrm{cm}$ and $t$ is in second. The phase difference between two positions of the same particle which are occupied at time interval of  $0.4 \mathrm{s}$ is

The equation of a wave of amplitude $0.02 \mathrm{m}$ and period $0.04 \mathrm{s}$ travelling along a stretched string with a velocity of $25 \mathrm{m} {\mathrm{s}}^{-1}$ will be

The path difference between the two waves, $y_1=A_1\sin \left(\omega t-\frac{2\pi x}{\lambda }\right)$ and $y_2=A_2\cos \left(\omega \mathrm{t}-\frac{2\pi \mathrm{x}}{\lambda }+\varphi \right)$ is