The decibel (dB) is the unit used to measure the intensity (I) of sound or noise level, and it is given in terms of a logarithmic function of a ratio of power intensities. In physics, the formula used for decibels is dB = 10 log10 (I/I1), where I1 is a reference value called the threshold of hearing intensity. In this equation, it is possible to express the intensity I as a multiple of I1.
To find different sound intensities or noise levels, it is a matter of using the formula. For example, find the sound intensity of a noise or a sound that is 1,000 times louder than the threshold intensity I1.
- Use the formula
- Express the logarithmic function as a power
Substitute into the formula 1000 x I1 for the intensity I to find that dB = 10 x log10 (1000 x I1)/I1, or 10 log101000.
Realize that log101000 is the same as 1000 = 10 y, or y =3. Replace 3 into the equation 10 x log101000 which becomes 10 x 3 and the sound intensity is equal to 30 dB.
On the decibel scale, the lowest sound intensity is 0 dB, which is near complete silence. A normal conversation is equivalent to an intensity of 60 dB, and a very noisy rock concert is about 110 dB. Noises or sounds that are at or above 85 dB can cause hearing problems. If a person listens to noises at this dB level for 8 hours, it can potentially cause hearing loss, as noted by the Centers for Disease Control and Prevention.