THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

3.12 Decibel Additions, Subtracting, and Averaging 51SolutionApplying Equation (3.24) we have for this caseL pt = 10 log(10 96/10 + 10 87/10 + 10 90/10 )= 97 dBIn certain situations, it is desirable to subtract an ambient or background noisefrom the total sound pressure level L pt in order to establish the sound pressurelevel L ps due to a particular source. Subtraction of decibels is analogous to theprocedure for their addition. The total sound pressure level L pt is converted intothe mean-square pressure ratio, as in Equation (3.23), and the background noiselevel L pB is measured simply by turning off the noise source. The mean-squarepressure ratio due to the background noise is obtained from( ) 2 pBL pB = 10 logp refor( ) 2 ( )pBL= logp −1 pB= 10 L pB /10ref 10The sound pressure level L ps of the source is found fromL ps = 10 log ( 10 L pt/10 − 10 L pB/10 ) (3.25)Example Problem 4Measurements indicated L pt = 93 dB at a specific location with a lathe in operation.When the lathe is shut down the background noise measures at 85 dB. Whatis the sound level due to the lathe?SolutionAccording to Equation (3.25), the noise level due to the lathe isL ps = 10 log(10 93/10 − 10 85/10 )= 92 dBA requirement may arise occasionally to find the average decibels in order todetermine the average sound pressure level L p . In some situations we may wishto measure the SPL at a single location several times and determine an averagevalue for engineering evaluation purposes. The procedure for averaging decibels isbased on the same premise for the summation and subtraction of decibels, namely,the application of Equation (3.22). Equation (3.24) for the addition of decibels is