The loudness level of a sound wave is a measure of its intensity or amplitude and is commonly expressed in decibels (dB). The dB scale is logarithmic, which means that it is not a linear representation of sound intensity.
The loudness level is relative to a reference level, which is typically the threshold of human hearing at a frequency of 1,000 Hz. This reference level is defined as 0 dB, and it corresponds to the quietest sound that the average human ear can perceive.
The formula to calculate the loudness level in decibels is:
L = 20 * log10(P/P0)
Where: L = loudness level in decibels P = sound wave pressure (amplitude) P0 = reference sound wave pressure (threshold of human hearing)
Since the scale is logarithmic, every increase of 10 dB corresponds to a tenfold increase in sound intensity. For example, a sound at 30 dB is ten times more intense than a sound at 20 dB.
It's important to note that the loudness level in decibels does not directly represent the perception of loudness by humans. Human perception of loudness is influenced by factors such as frequency and the characteristics of the sound wave. However, the dB scale provides a useful and standardized measure for comparing and quantifying sound levels.