Decibels

16.8. Decibels

The decibel (dB) is a measurement unit encountered frequently in connection with audio equipment. The main application of the decibel concept is for comparing two sound intensities. The intensity level b is defined as:

(16.10)

where I₀ is the intensity of the reference level to which I is being compared, and is often taken as the threshold of hearing, I₀ = 1.00 × 10^-12 W/m². Note that b is a dimensionless quantity and does NOT have units of W/m².

Example 12

The intensity level of the sound produced at a live rock concert is 120 dB above the threshold of hearing. What is the sound intensity I?

Use equation (16.10) with I₀ = 1.00 × 10^-12 W/m² and solve for the intensity I. We obtain

This represents a sound intensity that is one trillion times the threshold of hearing! However, the loudness will only be about 4100 times louder because each increase of 10 dB corresponds to a doubling of the loudness level. That is, a 10 dB sound will sound twice as loud as one which is 0 dB. A 20 dB sound is twice as loud as a 10 dB sound (four times louder than a 0 dB sound), and so on. Therefore, a 120 dB sound will appear about 2¹² or approximately 4100 times as loud as a 0 dB sound.