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Sound

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The distance at which a sound can be heard depends on its intensity. Intensity is the average rate of flow of energy per unit area perpendicular to the direction of propagation, similar to the rate at which a river flows through a gate in a dam. In the case of spherical sound waves spreading from a point source, the intensity varies inversely as the square of the distance, provided there is no loss of energy due to viscosity, heat conduction, or other absorption effects. Thunder, for example, is four times as intense at a distance of 1 km (0.6 mi) from the lightning bolt that caused it as it would be at a distance of 2 km (1.2 mi). In the actual propagation of sound through the atmosphere, changes in the physical properties of the air, such as temperature, pressure, and humidity, produce damping and scattering of the directed sound waves, so that the inverse-square law generally is not applicable in direct measurements of the intensity of sound.