The equation of a transverse wave traveling in a string is given by y(x,t) = 10 cos (π/2)(0.0050x - 8.0t + 0.57), in which x and y are expressed in centimeters and t in seconds. Write down the equation of a wave which, when added to the given one, would produce standing waves on the string.
y'(x,t) = [2ymcos(0.5β)]sin(kx - ωt+ 0.5β)
y'(x,t) = [2ym sin(kx)]cos(ωt)
The Attempt at a Solution
The problem is...I don't know what to do with that phase constant in the way. Like, I know that if the equation was just:
y(x,t) = 10 cos (π/2)(0.0050x - 8.0t)
I would just have to go through some really, really obnoxious trig to figure it out. But I am at a complete loss here. How do I even figure it out with that stupid phase constant around to muck things up?