6 One formula that indicates the vertical displacement of w

6 - One formula that indicates the vertical displacement of water as a function of position and time due to y av Asin( (x-vt) +0) Rewrite this formula in terms of parameters other than the constant and the waves wavelength . You can use parameters like the waves, period, velocity, frequency, angular frequency and so on, just not or A (5 pts)

Solution

given
y = Asin((2*pi/lambda)(x - vt) + phi)
now, agular frequency of the wave w = 2*pi*f
but f = v/lambda ( where v is wave speed)
hence
w = 2*pi*v/lambda

hence we can write
y = Asin((w/v)(x - vt) + phi)
y = Asin(wx/v - wt + phi)