Two atmospheric sound sources A and B emitisotropically at constant power. The s

Question

Two atmospheric sound sources A and B emitisotropically at constant power. The sound levels oftheir emissions are plotted in the figure below versus the radialdistance r from the sources. (a) What are the powers for these sound sources? (b) What are the sound intensities of these sources atr = 100 m? (c) Show that the difference in sound level is independent ofr. (d) What is the ratio of the larger power to the smallerpower? (e) Find the difference in the sources sound levels atr = 10 m. Two atmospheric sound sources A and B emitisotropically at constant power. The sound levels beta oftheir emissions are plotted in the figure below versus the radialdistance r from the sources. (a) What are the powers for these sound sources? (b) What are the sound intensities of these sources atr = 100 m? (c) Show that the difference in sound level is independent ofr. (d) What is the ratio of the larger power to the smallerpower? (e) Find the difference in the sources sound levels atr = 10 m.

Explanation / Answer

= 10log(I/Io) so I = Io*100.1 a) power P = I*4r2 =4r2Io*100.1 from the graph, A: r = 100 m, = 90 dB PA = 125.7 W B: r = 100 m, = 85 dB PB = 39.7 W b) IA = Io*108.5 =3.16*10-4 W/m2 IB = Io*109 = 1.00*10-3W/m2 c) = 10log(I/Io) =10log[P/(4r2Io)] A =10log[PA/(4r2Io)] =10logPA - 10log(4r2Io) B =10log[PB/(4r22Io)] = 10logPB -10log(4r2Io) A - B =10log(PA/PB) which is independent of r d) ratio k = PA/PB = 125.7/39.7 = 3.17 e) since A - B =10log(PA/PB) which is independent of r A - B (at r = 10 m) =A - B (at r = 100 m) = 90 - 85 =5 dB

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