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

3.14 Performance Indices for Environmental Noise 57by the equivalent summation:()1N∑L eq = 10 log 10 L n/10(3.29)Nn=1Here L n is acquired instrumentally for each of N equal intervals to yield L eq ,inthe course of digital processing of discrete samples.Example Problem 8Find L eq in the case where L n = 90.5, 95, 103, 88, and 98 dB(A) are obtained asthe respective average levels for five short, equal time intervals.SolutionFrom Equation (3.29)[ ]1Leq = log5 (1090.5/10 + 10 95/10 + 10 103/10 + 10 88/10 + 10 98/10 )= 97.9 dB(A)The day–night equivalent sound pressure level, L dn , essentially a modification ofL eq , was conceived for the purpose of evaluating community noise problems. Themodification consists of a nighttime penalty of 10 dB imposed on measurementsbetween 10 P.M. and 7 A.M. With time t given in hours, Equation (3.28) nowbecomes⎡ ⎛⎞⎤Ldn = 10 log ⎣ 110∫P.M.7A.M. ∫⎝ 10 L/10 dt + 10 (L+10)/10 dt⎠⎦ (3.30)247A.M.10 P.M.When the equivalent sound levels L eqd and L eqn are known for the day and nightperiods, respectively, the following version of Equation (3.30) can be used tocompute the day–night sound level:L dn = 10 logExample Problem 9[ 124(15 × 10 L eqd/10 + 9 × 10 (L eqn+10)/10 )] (3.31)Find L dn for the situation where the daytime equivalent sound level is 82 dB(A)and the nighttime equivalent sound level is 76 dB(A).SolutionInserting the appropriate values in Equation (3.31) we obtain[ ]182(76+10)Ldn = 10 log (15 × 10 10 + 9 × 10 10 ) = 84 dB(A)24