Final answer:
Decibels are represented by a logarithmic scale, reflecting a ratio relative to a reference intensity and aligning with the human perception of sound loudness.
Step-by-step explanation:
Decibels are represented by a logarithmic scale. The unit of decibel (dB) is used to express sound intensity level relative to a reference intensity. It is important to understand that while the intensity level is related to the perceived loudness of sound, it is not a direct measure of the physical intensity of the sound waves. Decibels represent one-tenth of the logarithm to base 10 of the ratio of two sound intensities, which aligns better with how human hearing perceives changes in sound intensity. The decibel level can be expressed mathematically as β(dB) = 10 log10(I/I0), where I is the sound intensity in watts per meter squared, and I0 = 10⁻¹² W/m² is the reference intensity set at the threshold of human hearing, which corresponds to 0 decibels. The term ‘deci’ in decibel actually means “one-tenth” reflecting that the number of decibels is ten times the logarithm to base 10 of the ratio of sound intensities.