Calculating Sound Wave Intensity and Decibels 10.0m from Source

[jamessmith]

A source of sound emits 5.0 mW of acoustic power uniformly in all directions.

1. Calculate the intensity of this sound wave 10.0 m from the source.
2. Find the sound level in decibles 10.0 m from the source.

Answers:
1. 4 x 10^-6 W/m^2 ---- I don't know how to get this answer.
2. 66 dB --- I don't know how to get this answer.

 

[irycio]

I don't really feel like calculating, but the idea behind this problem is very simple.
Consider a spherical loudspeaker, which probably doesn't exist, but it would definitely emit the sound in all directions. Thus, the acoustic wave would form a sphere. The power, that the wave carries with itself is constant, in this case it's your 5mW. The intensity you are supposed to calculate is the amount of power per square meter. 10.0m from the source the acoustic wave forms a sphere with radius=10 m. Now you just need to calculate the area of such spere and you should get the correct answer.

Now, having calculated that, you have to know what sound level (in dB) is. Mathematically, the equation is L=20log_10 (p1/p0). p1 is the acoustic pressure of the wave. You have been given the acoustic power of the wave. Now, according to the deffinition, P=W/t, but W=F*S (excuse this mid-school notation :P), hence P=F*S/t; but S/t=v, which is the velocity of the acoustic wave in the air-constant. Thus F=P/v. To get the pressure, divide by the area again. p0 is the refference value (dunno what it's called in English) equal to 2*10^(-5) Pa.

Hope it helps,
greets