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The fundamental wave equation


In a given medium, the waves propagate at a certain speed.

That is, the speed of a wave depends on the medium in which it propagates. For example, electromagnetic waves propagate in a vacuum at a speed of 300 000 km in a single second!

Let's relate wave propagation velocity to wave elements we have already seen: frequency and period.

We already know that for a given constant propagation velocity, that is, for a wave propagating without changing medium, we have:

on what: v is the speed;

is the distance traveled;

It is the time.

As we know, the period being the time required to produce a complete cycle, and the wavelength the width of a crest plus a valley, we can conclude that the wave travels a wavelength in a period.

on what: is the wavelength

T it's the period

f is the frequency

Follow the situation below, where we will relate the propagation speed, frequency and period of a wave.

A periodic wave produced on a string has a frequency of 20 Hz and a wavelength of 2 m. Calculate your speed.

Therefore, the speed of this wave is 40 m / s

Since the speed of a wave in a given medium is constant, we can see that if we increase the frequency, we decrease the wavelength, and vice versa.

We then conclude that frequency and wavelength are inversely proportional quantities.