Question

Two boats are anchored in the harbor, separated my a horizontal distance of 14m. The boats boo up and down as waves enter the harbor. When one boat is at its highest point, the other is at its lowest point and there are no crests between them. each boat makes exactly 5 complete up-and-down cycles every 15.0 s. the vertical distance between a boats highest and lowest position is 2.4m.
find the wavelength,
frequency, period, amplitude and speed

Answer 1

Given:

Horizontal distance between two boats = x = 14 m

One boat is at trough, the other is at crest.

As there is no crests between them meaning the boat are next to each other.

Wavelength is the distance between two consecutive crests/troughs = w

The distance between a crest and a trough next to it = w/2

Complete cycles = c = 5

Time taken for c cycles = t = 15 s

Vertical distance between two boats = y = 2.4 m

To find:

wavelength = w = 2x = 28 m

Amplitude =  A = Displacement from mean to extreme position = y/2 = 1.2 m

Time period for one cycle = T = t/c = 15/5 = 3 s/cycle

frequency = 1/T = 1/3 = 0.33 hertz

speed = wavelength/Period = w/T = 28/3 = 9.33 m/s