Sound Pressure and Amplifier Power

Notes about sound pressure, hearing, dBs and watts

The dynamic range of hearing reaches from a low whisper to the discomforting roar of a jet engine. This range equals a ratio of 1:1024!

Experience shows that large numbers cannot be handled easily. Therefore, a system has been developed to handle these large ratios in easy decibels. This system of number relations may be used to handle both electrical and acoustical values. Please note the following definitions:

Doubling a voltage or a current – for example from 1 to 2 volts – corresponds to an increase of 6 dB. Dividing the same voltage by two will result in a decrease of 6 dB.

Example: If the output level of an amplifier is raised by 18 dB, the actual output voltage is 8 times higher than the original one, and will raise from 2 to 16 volts.

Doubling the power (or loudness) follows a different ratio. An increase from 1 Watt to 2 Watts represents a raise of 3 dB!

This indicates that an increase of 6 dB represents 4 times the original power (see table)

Example: If the output power of an amplifier is increased by 18 dB, it’s been raised by a factor of 64 (!) => from 2 to 128 Watts for example.

This also indicates that raising the loudness by 1 dB will require 27% more output power. Doubling the loudness (3 dB) will result in 100% more output power.

While selecting an appropriate power amplifier, please note: Doubling the output power of an amplifier increases the loudness (SPL) by 3 dB. Unfortunately, this does not mean, that the impression of loudness is doubled as well. The human ear shows a varying sensitivity over frequency. Therefore, on average, we require 10 dB increase of SPL (loudness) to feel a subjective doubling of the loudness. This, however, will then require 10 times the output power of an amplifier – i.e. a 1000 W amplifier will seem (!) to be only twice as loud as a 100 Watt amp.

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  • Joachim Schwarz
    June 2005