Question

Two boats - Boat A and Boat B - are anchored a distance of 17.3 meters apart. The incoming water waves force the boats to oscillate up and down, making three complete cycles every 16.4 seconds. When Boat A is at its peak, Boat B is at its low point. There are never any wave crests between the two boats. The vertical distance between Boat A and Boat B at their extreme is 8 meters. Determine the wavelength (in meters), frequency (in Hertz), and speed (in meters/second) of the wave
wavelength:
frequency:
speed:

Answer 1

Refer to this picture makes explaining easier:
http://www.yourdictionary.com/images/computer/WAVELEN.GIF

1)
Period = units seconds = how long it takes for 1 cycle
therefore 20 seconds every cycle = period
Period = 20 seconds

2)
frequency:
frequency = 1 / period
f=1/T
f = 1/20seconds = 1/20 Hz = 0.05Hz


if u learn in math courses u should know how a sin/cos wave look like or else google it

wavelength is the distance between 1 pt and the identical point right when the wave repeats again so e.g. peak to peak point or trough to trough point or crest to crest or any value in between.
so you know from crest to trough is 24 metres because the question says so

so if you want crest to crest (peak to peak) it would be 2X peak to crest or u can visualize the mirror image i it.

3)
so wavelength = 2X24m = 48 metres


finally. Amplitude
you are given crest to trough = 18meters
this is always true: the crest-trough distance divide by 2 is amplitude

4)
amplitude = 18/2 = 9 meters