# Progressive Wave

- These waves propagate in the forward direction of medium with a finite velocity and energy and momentum are transmitted in the direction of propagation of waves without actual transmission of matter.
- In progressive waves, equal changes in pressure and density occur at all points of medium.
- Various forms of progressive wave function:
*y*=*A*sin (*Ï‰t*â€“*kx*)*y*=*A*sin*y*=*A*sin 2*y*=*A*sin (*vt*â€“*x*)*y*=*A*sin*Ï‰*

*Some Important Points*

- If the sign between
*t*and*x*terms is negative, the wave is propagating along positive*X*-axis and if the sign is positive then the wave moves in negative*X*-axis direction. - The coefficient of sin or cos functions, i.e., Argument of sin or cos function, i.e., (
*Ï‰t*â€“*kx*) = Phase. - The coefficient of
*t*gives angular frequency, =*vk*. - When a given wave passes from one medium to another, its frequency remains unchanged.

# Terminology related to progressive waves

**Wave number**(

*) = 1/Î».*

__n__Unit = meter

^{â€“1}; Dimension = [*L*^{â€“1}].**Propagation constant (**

*k*)*k*= =

and

**Wave velocity (**The velocity with which the crests and troughs or compression and rarefaction travel in a medium is defined as wave velocity

*v*)*v*= =

**Phase and phase difference**Phase of the wave is given by the argument of sine or cosine in the equation of wave. It is represented by

- At a given position (for fixed value of
*x*), phase changes with time (*t*).*dÏ†*= - At a given time (for fixed value of
*t*), phase changes with position (*x*).