CBSE Class 11-science Answered
what is correct wave equation
y=A sin(wt-kx) or y=Asin(kx-wt) ???
which & how above equation of waves will used especially in +ve x-direction
& -ve x-direction ???
y=A sin(wt-kx) or y=Asin(kx-wt) ???
which & how above equation of waves will used especially in +ve x-direction
& -ve x-direction ???
Asked by Ravikant | 16 Feb, 2016, 06:59: PM
Expert Answer
Consider a particle O, situated at the origin. It performs a S.H.M. of amplitude A, angular frequency ω and produces a simple harmonic wave in the medium.
Suppose that the wave travels in the positive direction of X-axis and the particle O starts from the mean position. The relation between the displacement (y) of the particle and its position (x) in the medium.
y = A sin ωt
The particles on the righ of O, will recieve the disturbance after sometime and hence they will progressively lag behind the phase.
For a particle P at a distance x from O,
y = A sin (ωt-α) ... (1)
where α is the phase lag of P w.r.t. O.
Since a path difference of λ corresponds to a phase difference of 2Π radian, a path difference of x will correspond to a phase difference of .
Thus, the phase difference = ×(path difference)
Therefore, the displacement of P at any instant is given by,
This is the equation of a one-dimensional simple harmonic progressive wave.
The quantity is called the propagation constant (K).
Hence the equation can be written as y = A sin (ωt - Kx). ... (3)
If the wave is travelling towards left, in the -ve direction of X-axis, the negative sign should be changed to a +ve sign and the equation is written as,
Answered by Faiza Lambe | 17 Feb, 2016, 10:07: AM
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