can you give me the derivation of y=Asin(wt-kx)?

As we know simplest wave is defined as displacement at nay point, P on it 

y = A sin(ωt)

where A = amplitude of wave

ω = angular frequency

Suppose wave velocity is v. If disturbance take time t to reach the point Q right side of P. Then there will be different phase of wave at that point. So, displacement at that point becomes.

y = A sin(ωt- ø)

If x is corresponding path difference, so

ø = (2Π/λ)x

So, displacement of wave at Q become

y(x,t) = A sin(ωt- (2Π/λ)x)

=> y(x,t) = A sin(ωt- kx)

Where k = (2Π/λ) = wave number

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