Wave equation#Spherical waves

The spherical wave is a regularly and evenly spreading from a source in all directions in a strictly concentric wave fronts wave (eg sound wave, light wave).

However, such a spherical wavefront produced treated ( here in the example of sound waves in air only under the assumption strongly idealized conditions, such as in a spherical radiator of zero order, ie, a "breathing " ball, as a source for radiation in a homogeneous isotropic medium ) in undisturbed propagation. If the starting point of a wave to display (transmitter) as a point, then the wave propagates in a homogeneous, isotropic medium as a spherical wave from, that is, the surfaces of equal phase are concentric with the transmitter located spherical surfaces have the same distances from each other. As can be seen, the energy density is distributed in the spherical wave sound on ever larger areas, ie it decreases with 1/r2 from. This results in a decrease of the wave amplitude or sound pressure with 1 / r. That given by the reciprocal square distance decrease of the energy density of a spherical wave is also called the quadratic power law of distance. In other words, one could also say that reduces the power density on an energetic quarter ( -6 dB ) and therefore the sound pressure level as well by 6 dB by the quadrupling of the surface with doubling of distance from the transmitter.

Acoustic spherical wave (sound )

For removal of acoustic pressure p and particle velocity v is valid in the far field when the distance is known from the measurement point to the transmitter with r:

All sound field parameters take in the far field after the 6- dB - distance law from having. That is, the size values ​​are halved each distance is doubled. The sound intensity decreases as the size of the sound energy is proportional to the square of the distance from the transmitter, because the continuously emitted from the sound source of sound power passes through a continuously enlarging surface of the sound intensity, which drops to the extent as the area increases. I ~ 1 / A ~ 1/r2.

The total sound power radiated remains in the theoretical model on an envelope around the globe sound source constant, ie, it is independent of the transmitter distance r.

Where:

• Sound power
• Sound intensity I
• Distance from the measuring point to the transmitter r
• Area A.

With increasing distance from the transmitter, the spherical waves plane wave fronts are becoming increasingly similar. Is characteristic of spherical waves that all sound field sizes on concentric shells around the center of the excitation channel are constant, while this, however, plane wave in levels are constant, which are perpendicular to the propagation direction of the wave motion.

A distinction is similar to electromagnetic spherical waves even with spherical sound waves between a near field (r <2 · λ ) and a far-field (r> 2 · λ ). The particle velocity v and the Schallauslenkung ξ take in the near field and the far field with with from. The sound pressure p increases, however, from the near and the far field with. In spherical sound field, the Fast consists of a real component and a reactive component -v ' v. The 1/r2-Abfall the Fast in the near field is caused mainly by the blind Fast ' v. At the sound radiation in the near field namely occurs in addition to the actual (active ) sound energy also a reactive energy component that is due to the so-called resonant medium mass about. This refers to the one air mass, which is very close to the sound source " wattlos " back and forth without any compression. As a result of this non-negligible mass effect of the resonating air comes between sound velocity and sound pressure on a phase shift, which is characteristic of the size of the reactive energy. See the web link for the sound velocity. In the plane sound field, the Fast consists only of its active component. The sound velocity is not to be confused with the speed of sound. , The sound velocity c is the speed at which the sonic energy propagates, while the sound velocity v is only the rate of change of the particles.