A boat is on a quiet lake 200 m from a paddle wheel that creates waves which pass the boat every 1.8 s with an amplitude of 3 cm.
A) If the wave velocity for water waves is 1.5 m/s, what is the wavelength?
B) Write an equation for the displacement of the water as a function of position and time
C)What is the amplitude of the wave if the boat is moved 60 m closer to the paddle wheel?
v = lambda/T
D = Asin(kx - wt)
k = 2pi/lambda
v = w/k
The Attempt at a Solution
A) I dont think this question is worded very clearly but I am assuming they mean that the period is 1.8 s
if that is true then v= lambda/T so lambda = Tv = 1.8s * 1.5 m/s = 2.7 m
B) D = Asin(kx-wt)
k = 2pi/lambda = 2pi/2.7 = 2.32
v = w/k so w = vk = 1.5 * 2.32 = 3.48
a is given as .03 m
so D = .03sin(2.32x-3.48t)
C) the wave is going 1.5 m/s so it goes 60 m in 60/1.5 = 40 s
D = .03sin(2.32*60 - 3.48 * 40) = .03sin(0) = 0
the water is flat at that point
I am not confident at all that I did this right. please help?