(1) These waves propagate in the forward direction of medium with a finite velocity.

(2) Energy and momentum are transmitted in the direction of propagation of waves without actual transmission of matter.

(3) In progressive waves, equal changes in pressure and density occurs at all points of medium.

 

where y = displacement             A = amplitude             w = angular frequency             n = frequency             k = propagation constant             T = time period             l = wave length             v = wave velocity             t = instantaneous time             x = position of particle from origin

(4) Various forms of progressive wave function.

 (a) 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.

(b) The coefficient of sin or cos functions i.e. Argument of sin or cos function i.e. (w t - kx) = Phase.

(c) The coefficient of t gives angular frequency (d) The coefficient of x gives propagation constant or wave number k=

(e) The ratio of coefficient of t to that of x gives wave or phase velocity. i.e. v =

(f) When a given wave passes from one medium to another its frequency does not change.

(g) From  v =  Þ   v  Q n = constant

(5) Some terms related to progressive waves

(i) Wave number  : The number of waves present in unit length is defined as the wave number  = .

Unit = meter^–1 ;       Dimension = [L^–1].

(ii) Propagation constant (k) :  k = (iii) Wave velocity (v) : The velocity with which the crests and troughs or compression and rarefaction travel in a medium, is defined as wave velocity v =

(iv) 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