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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 ???
Asked by Ravikant | 16 Feb, 2016, 06:59: PM
answered-by-expert 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 begin mathsize 14px style fraction numerator 2 πx over denominator straight lambda end fraction end style.
Thus, the phase difference = begin mathsize 14px style fraction numerator 2 pi over denominator straight lambda end fraction end style×(path difference)
begin mathsize 14px style therefore straight alpha equals fraction numerator 2 straight pi over denominator straight lambda end fraction straight x end style
Therefore, the displacement of P at any instant is given by,
begin mathsize 14px style straight y equals straight A space sin space open parentheses ωt minus fraction numerator 2 πx over denominator straight lambda end fraction close parentheses space space space space... space left parenthesis 2 right parenthesis end style
This is the equation of a one-dimensional simple harmonic progressive wave.
The quantity begin mathsize 14px style fraction numerator 2 straight pi over denominator straight lambda end fraction end style 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,
begin mathsize 14px style straight y equals straight A space sin space open parentheses ωt plus fraction numerator 2 πx over denominator straight lambda end fraction close parentheses end style
Answered by Faiza Lambe | 17 Feb, 2016, 10:07: AM
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