When we drive a loudspeaker with a fluctuating voltage output by an amplifier, if the voltage is a purely sinusoidal fluctuation at a single frequency, we hope that the loudspeaker will produce a sound at the same single frequency. However, most real loudspeakers are slightly non-linear<\/strong> in their response; the sound output is not always perfectly directly proportional to the voltage input. This means that some additional frequency components get produced in the sound output even when only a single frequency is applied to the input. This is sometimes called non-linear distortion<\/strong>.<\/p>\n Non-linearity in a hi-fi system produces unwanted distortion, but for the ear, non-linear behaviour is a critical feature that enables the large dynamic range of human hearing. The non-linearity of the ear has been known for over a century, but it was relatively recently that the primary causes of non-linearity have been identified. The middle ear is quite linear at normal listening levels. It is the inner ear non-linearity that produces distortion, which can be heard, and measured in the ear canal. In fact, the measurement of distortion products in the ear canal is used as a hearing test for newborn infants and children, since the distortion products are absent for certain forms of hearing impairment! But what is a distortion product ?<\/p>\n If two frequencies, f<\/em>1<\/sub> and f<\/em>2<\/sub>, are present in a sound, in principle, the ear non-linearity would produce intermodulation products equal to the sum and difference of the two frequencies, that is m<\/em> f<\/em>1<\/sub> = n<\/em> f<\/em>2<\/sub>, for any whole numbers m and n. In particular, it turns out that a difference tone of 2f<\/em>1<\/sub> – f<\/em>2<\/sub> is quite audible, for certain choices of frequencies. The demonstration below illustrates this phenomenon. It is simply a constant sine wave and a downward swept sine wave on two channels. Nonlinearities in the ear cause the listener to hear an intermodulation tone when both channels are played at the same time. As a result, a rising tone is heard. If you don’t notice it at first try increasing the volume of your loudspeakers.<\/p>\n\nDistortion (or intermodulation) products<\/h4>\n