The displacement of a particle in a medium is $y = 10^{-4} \sin(100t + 20x + \frac{\pi}{3}) \ m$,where $t$ is in seconds and $x$ is in metres. The speed of the wave is (in $m/s$)

If $\vec{u}$ is the instantaneous velocity of a particle and $\vec{v}$ is the velocity of the wave,then:

The phase difference between two waves represented by $y_1 = 10^{-6} \sin [100t + (x/50) + 0.5] \, m$ and $y_2 = 10^{-6} \cos [100t + (x/50)] \, m$,where $x$ is expressed in meters and $t$ is expressed in seconds,is approximately .... $rad$.

When a wave propagating in one medium enters another medium,which of the following characteristics remains constant?

The speed of a wave in a certain medium is $960\, m/s$. If $3600$ waves pass over a certain point of the medium in $1\, minute$,the wavelength is .... $metres$.

The figure below shows the wave $y = A \sin (\omega t - kx)$ at any instant traveling in the $+ve$ $x$-direction. What is the slope of the curve at $B$?