Intensity and loudness of sound
The intensity of a sound wave is defined as the rate of flow of energy per unit area perpendicular to the direction of the wave.
By mathematical treatment which is outside the scope of this book it may be shown that the intensity of a sound wave in air is proportional to: (a) the density of the air; (b) the square of the frequency; and (c) the square of the amplitude. From the practical point of view we have to take the density of the air as we find it, and, therefore, for a sound of given frequency the most important factor is the square of the amplitude. Consequently, when the amplitude of vibration of a tuning fork or loudspeaker diaphragm is doubled the sound energy is not doubled but made four times as great.
Obviously, the loudness of a sound will depend on the intensity, but it does not follow that loudness is directly proportional to intensity. In the first instance, loudness depends on the varying pressure exerted on the eardrum by the incoming wave, and this will depend on the energy conveyed by the wave. But this is not the only factor involved. The ear varies in its sensitivity to sounds of different frequencies. Generally speaking, the ear is more sensitive to the higher frequencies.