The equation of a wave travelling in a string can be written as $y=3\cos \pi (100t-x)$. Its wavelength is 

A plane progressive wave is represented by the equation $y=0.1\sin \left(200\pi t-\frac{20\pi x}{17}\right)$ where y is displacement in $\mathrm{m},\mathrm{t}$ in second and $\mathrm{x}$ is distance from a fixed origin in metre. The frequency, wavelength and speed of the wave respectively are 

The displacement y of a wave travelling in the x-direction is given by $y={10}^{-4}\sin \left(600t-2x+\frac{\pi }{3}\right)$ metres, where x is expressed in metres and $t$ in seconds. The speed of the wave-motion, in ${\mathrm{ms}}^{-1}$, is 

The equation of the progressive wave is $y=a\sin 2\pi \left(nt-\frac{x}{5}\right).$ The ratio of maximum particle velocity to wave velocity is 

The equation of the progressive wave is $Y=3\sin \left[\pi \left(\frac{t}{3}-\frac{x}{5}\right)+\frac{\pi }{4}\right]$ where x and Y are in metre and time in second. Which of the following is correct?

The equations of displacement of two waves are given as $y_1=10\sin \left(3\pi t+\frac{\pi }{3}\right)$, 
$y_2=5(\sin 3\pi t+\sqrt{3}\cos 3\pi t).$ Then what is the ratio of their amplitudes? 

The equation of $a$ wave is $y=60\cos (1800t-6x),$ where $y$ is in microns, $t$ in seconds and $x$ in metres. The ratio of maximum particle velocity to the wave velocity of wave propagation is 

A wave in a string has an amplitude of $2\mathrm{cm}$. The wave travels in the positive direction of $\mathrm{X}$-axis with a speed of $128 \mathrm{m} {\mathrm{s}}^{-1}$ and it is noted that $5$ complete waves fit in $4\mathrm{m}$ length of the string. The equation describing the wave is