$A$ travelling wave is described by the equation $y(x, t) = 0.05 \sin(8x - 4t) \; m$. The velocity of the wave is $..... \; m/s$ [all the quantities are in $SI$ units].

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

The disturbance $y(x, t)$ of a wave propagating in the positive $x$-direction is given by $y = \frac{1}{1 + x^2}$ at time $t = 0$ and by $y = \frac{1}{1 + (x - 1)^2}$ at $t = 2 \ s$,where $x$ and $y$ are in meters. The shape of the wave disturbance does not change during the propagation. The velocity of the wave in $m/s$ is:

$A$ longitudinal wave is represented by $x = 10 \sin 2 \pi (nt - \frac{x}{\lambda}) \, cm$. The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to .....................

$A$ travelling wave passes a point of observation. At this point,the time interval between successive crests is $0.2 \ s$. Which of the following is true?

$A$ small amplitude progressive wave in a stretched string has a speed of $100 \ cm/s$ and a frequency of $100 \ Hz$. The phase difference between two points $2.75 \ cm$ apart on the string,in radians,is