The loudness of a sound is expressed as a ratio comparing the sound to the least audible sound. The range of energy from the lowest sound that can be heard to a sound so loud that is produces pain rather than the sensation of hearing is so large that an exponential scale is used. The lowest possible sound that can be heard is called the threshold of hearing. The sound level at the threshold of hearing is:

Intensity of sound is measured in Watts per square meter. To calculate the intensity level in decibels, find the ratio of the intensity of sound to the threshold intensity. Since an exponential scale is being used, you will find the logarithm of the ratio. If you stopped at this point the intensity level would be expressed in Bels. This unit was named in recognition of Alexander Graham Bell. To express the intensity level in dB (deciBels) multiply the logarithm of the ratio by 10. The resulting equation is:

The intensity of sound in a classroom when no one is speaking is approximately:

Three steps are needed to calculate the decibel level of the sound given above:

1. Find the ratio of the sound intensity to the threshold intensity

2. Take the logarithm of the ratio

3. Multiply the ratio by 10

To find the intensity of a given sound whose intensity level in decibels is known, perform the above steps in reverse order and perform the inverse operation. For example a power lawnmower produces an intensity level of 100 dB. What is the intensity of the sound which produces an intensity level of 100 dB?

1. Divide the decibel level by 10

2. Use that value as the exponent of the ratio

3. Use that power of ten to find the intensity in Watts per square meter.

This equation reduces to: