urgent please help?

Question

in 1976 the who set a record for the ludest concert: the sound level 46 meters in front of the speaker system was 120 dB
a.) what was the intencity of the sound in watts
b.) what was the inensity described by someone 145 meters from the speaker?

Answer 1

The intesity at 36 meters was 120db. 120 = 10log(W/W0) where W0 = 10^-12 watt/m^2

12 = log(W/10^-12) = log(W*10^12); 10^12 = W*10^12, W = 1watt/m^2 At 46m there are 4*π*46^2 m^2 = 2.66*10^4 m^2. Therefore the total power output was 2.66*10^4 watts, or 26.6kw. (This assumes power was radiated equally in all directions, including down.)

The area at 145 m is 4*π*145^2 = 2.64*10^5 m^2; the sound intensity at that point is then 26.6*10^3w / 2.64*10^5 m^2 = 10.47*10^-2 w/m^2. In db that would be 10*log(10.47*10^-2/10^-12) = 110db