The Decibel

Saibal Ray
Centre for Sound Design

Perhaps the most useful tool ever created for audio practitioners is the decibel (dB). It allows changes in system parameters such as power, voltage, or distance to be related to level changes heard by a listener. In short, the decibel is a way to express “how much” in a way that is relevant to the human perception of loudness. Like most audio tools, it has been modified many times to stay current with the technological practices of the day. Excellent resources are available for that information. What follows is a short study on how to use the decibel for general audio work. 

Most of us tend to consider physical variables in linear terms. For instance, twice as much of a quantity produces twice the end result. Twice as much sand produces twice as much concrete. Twice as much flour produces twice as much bread. This linear relationship does not hold true for the human sense of hearing. Using that logic, twice the amplifier power should sound twice as loud. Unfortunately, this is not true. 

Perceived changes in the loudness and frequency of sound are based on the percentage change from some initial condition. This means that audio people are concerned with ratios. A given ratio always produces the same result. Subjective testing has shown that the power applied to a loudspeaker must be increased by about 26% to produce an audible change. Thus a ratio of 1.26:1 produces the minimum audible change, regardless of the initial power quantity. If the initial amount of power is 1 watt, then an increase to 1.26 watts (W) will produce a “just audible” increase. If the initial quantity is 100 W, then 126 W will be required to produce a just audible increase. A number scale can be linear with values like 1, 2, 3, 4, 5, etc. A number scale can be proportional with values like 1, 10, 100, 1000, etc. A scale that is calibrated proportionally is called a logarithmic scale. In fact, logarithm means “proportional numbers.” For simplicity, base 10 logarithms are used for audio work. Using amplifier power as an example, changes in level are determined by finding the ratio of change in the parameter of interest (e.g. wattage) and taking the base 10 logarithm. The resultant number is the level change between the two wattages expressed in Bels. The base 10 logarithm is determined using a look-up table or scientific calculator. The log conversion accomplishes two things: 

1. It puts the ratio on a proportional number scale that better correlates with human hearing. 

2. It allows very large numbers to be expressed in a more compact form. 

The final step in the decibel conversion is to scale the Bel quantity by a factor of ten. This step converts Bels to decibels and completes the conversion process.

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With a postgraduate diploma in film and television from SRFTII in Kolkata, Saibal Ray happens to be a Dolby Scholarship Holder. Having published three fictions, Saibal has worked with prestigious organizations such as SRFTII, Linear Electronics, Acoustics and Audio Video Solutions Pvt. Ltd., Ramoji Academy of Film and Television and Amity University. He was also a fellow member of Asian Film Academy in Busan in South Korea.