Two waves are represented by the equations $y_1 = A \sin (\omega t + kx + 0.57) \ m$ and $y_2 = A \cos (\omega t + kx) \ m$,where $x$ is in metre and $t$ is in second. What is the phase difference between them?

Two sound waves having a phase difference of $60^{\circ}$ have a path difference of

$A$ 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 ............ $m$.

Define the angular wave number and provide its mathematical equation.

Write the equation of the relation between wave speed $(v)$,angular frequency $(\omega)$,and angular wave number $(k)$.

The phase difference between two points separated by $1 \ m$ in a wave of frequency $120 \ Hz$ is $90^o$. The wave velocity is .... $m/s$.