Wavefront. Multi-dimensional waves. Plane waves

Waves can be classified into different categories depending on the dimensions in which they can travel. When they travel along just one dimension they are called one-dimensional (for instance, waves propagating along a rope or a string and sound waves propagating through a cylinder containing a gas).
A wave that travels in two dimensions is called two-dimensional, such as the waves shown in the picture below produced by a dropping an object into still water.

The waves produced by a musical instrument are three-dimensional waves because they can travel in the three dimensions of space.

In order to visualize the propagation of a wave it is useful to introduce the concept of wavefront.

Wavefront is a line (or surface) on which every point has the same phase.

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For a one dimensional wave, the wavefront would be just a point; for a two-dimensional wave such as the one shown in the picture above, wavefronts are circumferences. The wavefronts of a sound wave propagating along a homogeneous and isotropic medium is a sphere centered at the source. This is why such waves are called spherical waves.

The distance between two consecutive wavefronts is called the wavelength λ of the wave. The rays (in red in the figure below) are arrows pointing in the direction waves are moving, and are always perpendicular to the wavefronts.

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Plane wave

At great distances from the source, a small part of a spherical wavefront can be approximated by a plane, as shown in the figure below. In this case we have a plane wave.

The mathematical description of a plane wave is the same as that of a one-dimensional harmonic wave :

where A is the amplitude, ω the angular frequency and k the wavenumber.

Check out the page intensity of a sound wave to know more about the energy carried by a wave.

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