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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:
    1. y = A sin (ωtkx)
    2. y = A sin 32201.png
    3. y = A sin 232195.png
    4. y = A sin 32189.png(vtx)
    5. y = A sin ω 32183.png
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., (ωt – kx) = Phase.
  • The coefficient of t gives angular frequency, 33390.pngvk.
  • When a given wave passes from one medium to another, its frequency remains unchanged.

Terminology related to progressive waves

Wave number () The number of waves present in unit length is defined as the wave number (n) = 1/λ.
Unit = meter–1; Dimension = [L–1].
Propagation constant (k)
k = 32152.png = 32145.png
32138.png and 32132.png
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 = 32126.png = 32120.png
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).
    ⇒  = 32102.png
    ⇒ Phase difference =32095.png Time difference
  • At a given time (for fixed value of t), phase changes with position (x).
    ⇒ Phase difference = 32082.png Path difference
    Time difference = 32076.png× Path difference

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