$A$ simple harmonic progressive wave is represented as $y = 0.03 \sin \pi (2 t - 0.01 x) \ m$. At a given instant of time,the phase difference between two particles $25 \ m$ apart is

Two simple harmonic progressive waves have displacements $y_1 = a_1 \sin \left(\frac{2 \pi x}{\lambda} - \omega t\right)$ and $y_2 = a_2 \cos \left(\frac{2 \pi x}{\lambda} - \omega t + \phi\right)$. What is the phase difference between the two waves?

$A$ transverse wave of frequency $500 \,Hz$ and speed $100 \,m/s$ is travelling in the positive $x$-direction on a long string. At time $t=0 \,s$,the displacements at $x=0.0 \,m$ and at $x=0.25 \,m$ are $0.0 \,m$ and $0.02 \,m$,respectively. The displacement at $x=0.2 \,m$ at $t=5 \times 10^{-4} \,s$ is ............ $m$.

The equation of a wave is given by $y = 10 \sin \left(\frac{2 \pi t}{30} + \alpha\right)$. If the displacement is $5 \ cm$ at $t = 0 \ s$,then the total phase angle at $t = 7.5 \ s$ will be:

An equation of a simple harmonic progressive wave is given by $y=A \sin (100 \pi t-3 x)$. The distance between two particles having a phase difference of $\frac{\pi}{18}$ in meters is:

The figure given shows a sinusoidal wave on a string. If the frequency of the wave is $150 \, Hz$,what is the wavelength and velocity of the given wave?