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Rocking the Boat - help1

A wave property has a precise meaning. The wavelength is the distance between two adjacent crests. The frequency is the number of vibrational cycles per time. The period (reciprocal of the frequency) is the time for one vibrational cycle. The amplitiude is the vertical distance from the resting position to the crest. The speed tells how fast the wave moves and is calculated as frequency multiplied by wavelength.

There are three similar versions of this question. Here is one of the versions:

Version 1:

Two boats are anchored in the harbor, separated by a horizontal distance of 12 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 2 complete up-and-down cycles every 10.0 s. The vertical distance between a boat's highest and lowest position is 2.4 m. Complete the diagram, showing where the second boat is located. Then determine the wavelength (m), frequency (Hz), period (s), amplitude (m), and speed (m/s) of the waves.

Completing the Diagram
Each question in this Question Group describes one boat being at its highest point and the other boat being at its lowest point with no wave crests positioned between them. And so the second boat is located in the first trough.

Determining the Wavelength
Your diagram is essential. It shows one boat on a crest and the second boat in a trough. The wavelength can be thought of as the horizontal distance from crest to crest. The trough - where the second boat is located - is one-half of a wavelength from the crest where the first boat is located. So the horizontal distance between boats is equal to one-half wavelength. You can double this distance to get the complete wavelength.

Determining the Frequency and Period
Frequency and period have a reciprocal relationship. If you know one of these quantities, then you can calculate the other by taking the reciprocal. The problem states the number of complete up and down cycles in a given amount of time. Frequency can be thought of as cycles per second. So dividing the number of cycles by the number of seconds will provide a frequency value. Period can be thought of as the seconds per one cycle. So dividing the number of seconds by the number of cycles will provide the period value.

Determining the Amplitude
The problem states the vertical distance between a boat's highest and lowest position. This distance refers to the vertical distance between a crest and a trough. The resting position is the halfway point between the crest and the trough. An amplitude measurement is made from this resting position up to the crest ("distance from rest to crest"). And so the value that is given is two times the amplitude. You can use this relationship to calculate the amplitude.

Determining the Speed
Determining the speed of a wave is quite easy if the frequency and wavelength are known. It is a simple matter of multiplying frequency (in Hz) by wavelength (in m).

Try these links to The Physics Classroom Tutorial for more help with understanding wave properties:

The Anatomy of a Wave (wavelength and amplitude)

Frequency and Period of Waves

The Wave Equation