Progressive wave

A progressive mechanical wave is a perturbation that propagates from one point to the next without any transport of matter, but with transport of energy.

Waves on the surface of water….a sound wave ….or a seismic wave are examples of progressive waves in  2 or 3 dimensions.

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This simulation illustrates the particular case of a one dimensional progressive wave. The perturbation generated by the source is found farther away … an instant later.

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We measure here that the wave gets to 0.8m on the abscissa after 4s. From this we can determine the velocity, “v” of the wave, also called its celerity.

The value of v is a property of the medium of propagation.

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If  the source of excitation is periodic, the wave that is propagated  is a periodic progressive wave.

Let’s study the sinusoidal wave. It is characterized by a double periodicity:

• A spatial periodicity that we call the wavelength
• and  a temporal periodicity which is its period.

To measure the wavelength, let’s freeze time and measure the distance that separates two consecutive peaks.

…  We also observe that two points one wavelength apart vibrate in phase.

To determine the period, we freeze x and watch the vibration of a single point.

The time required for the red ball to complete one cycle is the period.

Note that the period is also the time needed  for the wave to travel the distance λ.

Using these observations, we can determine the speed of the wave v = λ/t, or also, λ.f,  if we introduce the frequency f, which is the inverse of the period expressed in units  of Hertz.