(1) These rays transfer in the forward direction of medium with a finite speed.
(2) Energy and momentum are transferred in the direction of propagation of waves without real transmission of matter.
(3) In progressive pulse, equal changes in density and pressure happens at each points of medium.
(4) Several forms of progressive wave function:
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(i) y = A sin (w t - kx)
(ii) y = A sin {w t -(2π/λ)x}
(iii) y = A sin 2π(t/T -x/λ)
(iv) y = A sin 2π/λ(vt - x)
(v) y = A sin ω(t - x/v)
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where y = displacement
A = amplitude
ω = angular frequency
n = frequency
k = propagation constant
T = time period
λ = wave length
v = wave velocity
t = instantaneous time
x = position of particle from origin
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Important points:
(a) If the sign between x and t terms is negative the ray is propagating along positive X-axis and if the signature is positive then the wave goes in negative X-axis.
(b) The coefficient of cos or sin functions i.e. Argument of sin or cos function i.e. (ωt - kx) = Phase.
(c) The coefficient of t provides angular frequency ω = 2πn = 2π/T= vk.
(d) The coefficient of x provides propagation constant or ray number k = 2π/λ = ω/v.
(e) The ratio of coefficient of t to that of x provides wave or phase velocity. i.e. v = ω/k .
(f) When a given wave passes from one phase to another its frequency does not modifies.
(g) From v = nλ => v ∝ λ n = constant .
(5) Some terms related to progressive pulses
(i) Wave number : The number of waves appear in unit length is described as the pulse number = 1/λ.
Unit = meter-1 ; Dimension = [L-1].
(ii) Propagation constant (k) : k = Φ/x = Phase diffrence between particals/distance between them
k = ω/v and k = 2π/λ
(iii) Wave velocity (v) : The velocity with which the troughs and crests or compression and rarefaction goes in a phase, is described as wave speed v =ω/k = nλ = ωλ/2π = λ/T.
(iv) Phase and phase difference : Phase of the wave is shown by the argument of sine or cosine in the relation of wave. It is denoted by Φ(x,t) = 2π/λ(vt-x).
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