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# Demonstration of Relative Loudness

Author: N.H. Crowhurst

 With an ordinary linear resistor loudness does not vary in proportion to rotation

This fact of the logarithmic sensation of loudness can be very easily demonstrated with a simple test, using an amplifier with a separate volume control and a loudspeaker. (A volume control is a resistor with a sliding contact; if an audio program is fed through the resistor and only part of it is picked off by means of the slider, the volume can be changed by moving the slider.) If the volume control is an ordinary variable resistor (with the resistance uniformly distributed), the intensity will be proportional to the angle between the slider position and the "zero" position. Using this kind of resistor for a volume control, the loudness does not sound as if it varies in direct proportion at all. In the first few degrees of rotation there is a big change in loudness, but further rotation makes hardly any additional change.

 Comparison of uniform and logarithmic resistors.

For this reason, variable resistors intended for use as volume controls are made differently. The resistance is not uniformly distributed, but rather is proportional to the logarithm of the angle of rotation from the zero end. Thus 50° of movement of the slider allows the passage of one-thousandth of a volt of audio signal; 100° may produce one-hundredth of a volt; 150°, one-tenth of a volt; 200°, one volt, and so on. When this kind of control is used, the volume, or loudness, seems to be proportional to the amount of rotation of the control.

Last Update: 2010-11-03