![]() The intensity varies inversely with the square of the distance from the source. The mathematical relationship between intensity and distance is sometimes referred to as an inverse square relationship. Since energy is conserved and the area through which this energy is transported is increasing, the intensity (being a quantity that is measured on a per area basis) must decrease. The diagram at the right shows that the sound wave in a 2-dimensional medium is spreading out in space over a circular pattern. The decrease in intensity with increasing distance is explained by the fact that the wave is spreading out over a circular (2 dimensions) or spherical (3 dimensions) surface and thus the energy of the sound wave is being distributed over a greater surface area. Typical units for expressing the intensity of a sound wave are Watts/meter 2.Īs a sound wave carries its energy through a two-dimensional or three-dimensional medium, the intensity of the sound wave decreases with increasing distance from the source. ![]() Intensity is the energy/time/area and since the energy/time ratio is equivalent to the quantity power, intensity is simply the power/area. The greater the amplitude of vibrations of the particles of the medium, the greater the rate at which energy is transported through it, and the more intense that the sound wave is. The amount of energy that is transported past a given area of the medium per unit of time is known as the intensity of the sound wave. This relationship between energy and amplitude was discussed in more detail in a previous unit. Subsequently, the amplitude of vibration of the particles of the medium is increased, corresponding to an increased amount of energy being carried by the particles. The greater amplitude of vibration of the guitar string thus imparts more energy to the medium, causing air particles to be displaced a greater distance from their rest position. If more energy is put into the plucking of the string (that is, more work is done to displace the string a greater amount from its rest position), then the string vibrates with a greater amplitude. The amount of energy that is transferred to the medium is dependent upon the amplitude of vibrations of the guitar string. The energy that is carried by the disturbance was originally imparted to the medium by the vibrating string. The disturbance then travels from particle to particle through the medium, transporting energy as it moves. For example, a vibrating guitar string forces surrounding air molecules to be compressed and expanded, creating a pressure disturbance consisting of an alternating pattern of compressions and rarefactions. The decrease goes as r squared because the area over which the light is spread is proportional to the distance squared.Sound waves are introduced into a medium by the vibration of an object. Notice that as the distance increases, the light must spread out over a larger surface and the surface brightness decreases in accordance with a "one over r squared" relationship. ![]() This relationship can be illustrated by the diagram below, which shows the apparent brightness of a source with luminosity L 0 at distances r, 2r, 3r, etc. Suppose that some time later the brightness of the light is either greater or lesser if the intensity diminished you would know that the source was moving away from you and if it became brighter you would know that the source was moving towards you (assuming the light source itself remained the same). ![]() Suppose you were to use a light meter to measure an initial intensity I i, or brightness, a distance r from a light source. The intensity or brightness of light as a function of the distance from the light source follows an inverse square relationship. More on Brightness as a Function of Distance ![]()
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