Loudness is psychological response to a sound. It depends on both the intensity and the frequency of the sound. As a rule of thumb, a doubling in loudness is approximately associated with an increase in sound level of 10 dB. (this rule of thumb is relatively inaccurate at very low or very high frequencis.) If the loudness of the machines in illustration 6. is to be doubled, how many machines at the same distance from the worker must be running?

Explanation

using the rule of thumb, a doubling of loudness corresponds to a sound level increase of dB. Therefore,
`beta_2-beta_1=10dB=10log((I_2)/(I_0))-10log((I_1)/(I_0))=10log((I_2)/(I_1))`
Therefore, 10 machines must be operating to double the loudness.