# A water wave has a wavelength of 4.0 m and a speed of 2.0 m/s. What is the period of this wave?

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We know from wave theory that all waves have certain physical criteria. Waves have an amplitude, which for mechanical waves such as water waves, represents a measure of the amount of energy being transmitted by the wave.

Waves have a wavelength (Greek letter lambda) which is the distance between the adjacent portions of the wave which represent the repetition of the wave pattern. Usually wavelength is measured between two easily identifiable points of the wave such as from peak to peak, or trough to trough, of the wave.

Waves have a frequency (f) which is determined by the vibration of the source of the wave. The frequency of a wave is typically measured in cycles per second or Hertz (Hz) and is defined as the number of wavelengths that can pass a point in one second.

Waves also have a period (T) which is the amount of time (usually in seconds) it takes for an entire wavelength to pass by a given point.

Waves travel distances in time so they also have a wave speed.

These quantities are related to each other. The period and frequency are inversely related to each other. That is T = (1/f) and f = (1/T). The wave speed is determined from S = wavelengthxfrequency = wavelength/period

Thus we can find the period by solving the last equation for the period:

T = wavelength/S

For this example T = 4.0m/(2.0m/s) = 2.0 second (which produces a frequency of 0.50 Hz)