Wave Motion - Mission WM2 Detailed Help

Two boats - Boat A and Boat B - are anchored a distance of 20 meters apart. The incoming water waves force the boats to oscillate up and down, making one complete cycle every 10 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. The wavelength is ___ m, the period is ___ s, the frequency is ___ Hz, and the amplitude is ___ m. (HINT: begin with a diagram.)


 
Definition of Wave Quantities:

The wavelength of a wave is the length of the wave. It is often measured as the distance between two consecutive crests.

The amplitude of a wave is the maximum amount of displacement a point on a medium is makes relative to its resting position. It is often measured as the distance between the resting position and a crest position.

The frequency of a wave is the number of cycles occurring per unit of time. See Formula Frenzy section.

The period of a wave is the time elapsed between cycles. See Formula Frenzy section.


 
The reciprocal nature of frequency (f) and period(T) are seen in the following mathematical definitions. 

f = # of cycles / time        T = amount of time / cycle


 
This question will certainly give your understanding of the various wave quantities a real workout. Begin by constructing a diagram of the situation - draw a straight line for the resting position of the water surface. Then draw the familiar wave pattern which depicts the presence of a wave on the water surface. Position Boats A and B, with Boat A being at a crest position and Boat B being at a trough position. Label the horizontal distance between them and the vertical distance between them. Then ask, what is the wavelength? and what is the amplitude? Review the definitions of these terms if necessary. See Define Help section.