This type of scale is sometimes referred to as a logarithmic scale. Since the range of intensities that the human ear can detect is so large, the scale that is frequently used by physicists to measure intensity is a scale based on powers of 10. The most intense sound that the ear can safely detect without suffering any physical damage is more than one billion times more intense than the threshold of hearing. WOW! This faintest sound that a human ear can detect is known as the threshold of hearing (TOH). A sound with an intensity of 1*10 -12 W/m 2 corresponds to a sound that will displace particles of air by a mere one-billionth of a centimeter. This intensity corresponds to a pressure wave in which a compression of the particles of the medium increases the air pressure in that compressional region by a mere 0.3 billionth of an atmosphere. The faintest sound that the typical human ear can detect has an intensity of 1*10 -12 W/m 2. Humans are equipped with very sensitive ears capable of detecting sound waves of extremely low intensity. The Threshold of Hearing and the Decibel Scale The sample data in the table below illustrate the inverse square relationship between power and distance. And since the intensity-distance relationship is an inverse square relationship, whatever factor by which the distance is increased, the intensity is decreased by a factor equal to the square of the distance change factor. Since the intensity-distance relationship is an inverse relationship, an increase in one quantity corresponds to a decrease in the other quantity. Applied to the diagram at the right, the intensity at point B is one-fourth the intensity as point A and the intensity at point C is one-sixteenth the intensity at point A. Similarly, if the distance from the source is quadrupled, then the intensity is decreased by a factor of 16. So if the distance from the source is doubled (increased by a factor of 2), then the intensity is quartered (decreased by a factor of 4). 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. Sound waves are introduced into a medium by the vibration of an object.

Light intensity reduction equation