Two identical machines are positioned the same distance from a worker. The intensity of sound delivered by each operating machine at the worker's location is `2.0xx10^-7(W)/(m^2)`. (a) Find the sound level heard by the worker when one machine is operating. (b) Find the sound level heard by the worker when both the machines are operating.

Explanation

Imagine a situation in which one source of sound is active, and is then joined by a second identical source. Such as one person speaking and then a second person speaking at the same time or one musical instrument playing, and then being joined by a second instrument.
a. The sound level at the worker's location with one machine operating is given by
`beta_1=10((2.0xx10^-7(W)/(m^2))/(1.00xx10^(-12)(W)/(m^2)))=10log(2.0xx10^5)=53dB`
b. The sound level at the worker's location with double the intensity is given by
`beta_2=10log((4.0xx10^-7(W)/(m^2))/(1.00xx10^(-12)(W)/(m^2)))`
`=10log(4.0xx10^5)=56dB`
These results show that when the intensity is doubled the sound level increases by only 3 dB.