Imagine you are sitting on a surfboard in the ocean, waiting to catch a big wave. When the ocean is still, you are sitting at a point that would be the midpoint (the undisturbed position) of any waves that come your way. You look out to see and see a set of waves coming your way. What you see is actually a pattern of troughs followed be crests of the waves moving toward you and the shore. The distance between the crests is 5 meters. A crest passes you every 20 seconds. Answer these questions:

a. What is the wavelength?

b. What is the frequency?

c. What is the wave velocity?

The wavelength of a wave (represented with [tex]\lambda[/tex]) is the smallest distance between two points of the wave having the same shape. For instance, it can be measured as the distance between two consecutive crests of a wave (or the distance between two consecutive troughs).

For the wave in this problem, we have that the distance between the crests is 5 metres.

Therefore, the wavelength corresponds to this distance:

[tex]\lambda = 5 m[/tex]

2)

The frequency of a wave (represented with [tex]f[/tex]) is the number of complete cycles of the wave per unit time.

The frequency can be calculated as the number of crests of the wave (N) passing a given point per second:

[tex]f=\frac{N}{t}[/tex]

where t is the time.

The frequency can also be calculated as the reciprocal of the period (T), which is the time the wave takes for one complete oscillation:

[tex]f=\frac{1}{T}[/tex]

For the wave in this problem, one crest passes you every 20 seconds: this means that the period of the wave is 20 seconds,

T = 20 s

So the frequency is

[tex]f=\frac{1}{20}=0.05 Hz[/tex]

3)

The velocity of a wave is given by the wave equation:

[tex]v=f \lambda[/tex]

where

f is the frequency of the wave

[tex]\lambda[/tex] is its wavelength

For the wave in the problem,

f = 0.05 Hz

[tex]\lambda = 5 m[/tex]

Substituting,

[tex]v=(0.05)(5)=0.25 m/s[/tex]

Learn more about waves:

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