What is a Spherical Wave?

A spherical wave is a type of wave that emanates from a single point and expands uniformly in all directions. This wave can occur in various forms of waves, including sound waves, electromagnetic waves, and water waves. A spherical wave may have a time-varying amplitude, frequency, and phase. It is also known as a radiation pattern, which describes the directional dependence of radiation emitted by a source.

A spherical wave has a unique property that it does not have a preferred direction of propagation. It means that the wavefronts, which are the surfaces of constant phase, are always concentric spheres around the source. Another property is that the intensity of the wave decreases as it moves away from the source. In other words, the energy in a spherical wave is spread out equally over the surface of the sphere.

Properties of Spherical Waves

The property of a spherical wave is that it has a spherical symmetry. It means that the wave remains the same in all directions and has the same strength. The intensity of a spherical wave decreases as the distance from the source increases, following the inverse-square law.

Another property of spherical waves is that they can be coherent, meaning that they have a constant phase relationship between two or more waves. Coherent spherical waves can form interference patterns, where the intensity of the wave is either increased or reduced, depending on the phase relationship.

Applications of Spherical Waves

Spherical waves have several practical applications in different fields. In acoustics, spherical waves are used to model the sound field generated by a source, such as a loudspeaker or musical instrument. In optics, spherical waves are used to describe the propagation of light, including diffraction and interference phenomena.

Spherical waves are also used in radar and sonar systems to detect and locate objects. For example, sonar systems transmit spherical waves through water and receive the echoes returned from submerged objects to determine their location and size.

Example of Spherical Wave in Real Life

One of the examples of a spherical wave in real life is the sound wave generated by a firework explosion. When a firework explodes, it creates a sound wave that expands uniformly in all directions, forming a spherical wavefront. As the wavefronts move away from the source, the intensity of the sound decreases, and the sound becomes quieter.

Another example of a spherical wave is the ripples formed on the surface of a pond when a stone is thrown into it. The waves produced by the stone expand uniformly in all directions, forming a series of concentric circles on the surface of the water. As the waves move away from the source, their amplitude decreases, and the ripples become smaller until they disappear.