A source has a SPL Re 20106 Pa of 80 dB at 100 meters What i

A source has a SPL (Re: 20*10^-6 Pa) of 80 dB at 100 meters. What is the sound pressure
level at 600 meters if the source radiates spherically? What is the level at 160
meters? At what distance is the level 100 dB? At what distance is the level 50 dB?

Solution

SPL = 80 dB at 100 m

dB = 20 log10(P1/Pref)= P1 = 0.2 Pa

p2= p1* r1/r2= 0.2*100/600 = 0.03333

Decibel level = 64.4369 dB

p3= p1*r1/r3 = 0.2*100/160 = 0.125 Pa

Decibel level = 75.9176 dB

100/20 = log10 (p4/pref)

2*10^-5*10^5 = p4 = 2 Pa

p4 *r4 = p1 *r1 => r4 = 0.2*100/2 = 10 m

50/20 =  log10 (p5/pref)

p5 = 6.324*10^-3 Pa

p5 * r5 = p1 * r1= r5 = 3162.2776 m