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

Solution14.12 Gas-Jet Noise 391Using Equation (14.44),( ) ( T (260 + 273.2) ◦ )K T = 20 log = 20 log= 5.2dBT a (20 + 273.2) ◦ KThe temperature-corrected sound power level becomesL W = 107.6 + 5.2 = 112.8dBWhen the overall power of a jet is determined, the overall sound pressure at anylocation in region surrounding the jet can be estimated through the use of therelationship between L p and L W :( ) Q(θ,φ)L p = L W + 10 log= L4π r 2 W + 10 log [Q(θ,φ)] − 20 log r − 11(14.45)where Q(θ,φ) is the directivity in three-dimensional space, and r is the distancefrom the source of L W to the location where the value of L p is desired. Thedirectivity index DI is given by( ) Q(θ,φ)DI = 10 log4π r 2In many cases of interest, the jet can be generally regarded as a point source withtypical directionality as shown in Figure 14.13. The parameter φ can be disregardedin axisymmetric flows.Figure 14.13. A fairly typical configuration for directivity DI Q in a small subsonic jet.Note that the peak levels occur approximately in the angular range of 15 ◦ to 45 ◦ from thecentral axis of the jet.