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