Question

Two boats are anchored in the harbor, separated by a horizontal distance of 24 m.

The boats bob 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 wave crests between
them. Each boat makes exactly 4 complete up-and-down cycles every 12.0 S. The
vertical distance between a boat's highest and lowest position is 3.6 m.
Determine the wavelength, frequency, period, amplitude and speed of the waves.
Include at least two significant digits on your answer.
Wavelength (m):
Frequency (Hz):
Period (s):
Amplitude (m):
Speed (m/s):​

Answer 1

Horizontal distance between two boats = x = 24m
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 = 4
Time taken for c cycles = t = 12s
Vertical distance between two boats = y = 3.6m

To find:
wavelength = w = 2(x) = 48m
Amplitude = A = Displacement from mean to extreme position = y/2 = 1.8m
Time period for one cycle = T = t/c = 12/4 = 3 s/cycle
frequency = 1/T = 1/3 = 0.33 hertz
speed = wavelength/Period = w/T = 48/3 = 16m/s