Tom at a beach sees an anchored fishing boat rise and fall 3.5 m once every 4.0 s as wave crests 25 m apart pass through

Question

Tom at a beach sees an anchored fishing boat rise and fall 4.5 m once every 5.0 s as wave crests 25 m apart pass through it

(a) Calculate the frequency of the waves. (b) Calculate the speed of waves. (c) Calculate the speed of individual water molecules on the surface of water

Answer 1

The Period of the wave is 5 s so the frequency = 1/T = 0.2 Hz

We know velocity = freq x wavelength = 0.2 x 25 m = 5 m/s

For the velocity of the molecules we know v =-Aω(Sin(ωt))

If we are just interested in the max speed we can ignore the sine function v =Aω

where ω = 2πf = 31.42 and A is the amplitude = 4.5/2

Therefore the max speed of the molecules is 70.7 m/s