afcwestwarrior
Mar8-09, 02:31 PM
1. The problem statement, all variables and given/known data
A certain sound wave has a measured intensity of 40 decibels at a distance of 125 m from the point source where the waves originated. At what distance from the source would the intensity be increased to 70 decibels.
2. Relevant equations
Sound Level (B) = 10 decibels log ( I/ Io)
I = Ps / 4 pi (r^2)
3. The attempt at a solution
40/ 10 = log (I/Io)
10^4 = I / Io
10 ^4 (Io) = I
10 ^4 (Io) = Ps / 4 pi (r^2)
Ps = 10 ^4 (Io) 4 pi (r^2)
so we then we find the new radius
70/10 = log (I/Io)
10^ 7 ( Io) = I
10^ 7 ( Io) = Ps / 4 pi (r^2)
solve for r 2
r2 = √ (Ps / 4 pi (10^7) I o)
r2 = √ (10 ^4 (Io) 4 pi (r^2) ) / (4 pi (10^7) I o)
= 3.9 m
Shouldn't the radius increase by much more. Because 70 Decibels is much louder than 40 Decibels.
I'd figure that it would be by 50 meters or something.
A certain sound wave has a measured intensity of 40 decibels at a distance of 125 m from the point source where the waves originated. At what distance from the source would the intensity be increased to 70 decibels.
2. Relevant equations
Sound Level (B) = 10 decibels log ( I/ Io)
I = Ps / 4 pi (r^2)
3. The attempt at a solution
40/ 10 = log (I/Io)
10^4 = I / Io
10 ^4 (Io) = I
10 ^4 (Io) = Ps / 4 pi (r^2)
Ps = 10 ^4 (Io) 4 pi (r^2)
so we then we find the new radius
70/10 = log (I/Io)
10^ 7 ( Io) = I
10^ 7 ( Io) = Ps / 4 pi (r^2)
solve for r 2
r2 = √ (Ps / 4 pi (10^7) I o)
r2 = √ (10 ^4 (Io) 4 pi (r^2) ) / (4 pi (10^7) I o)
= 3.9 m
Shouldn't the radius increase by much more. Because 70 Decibels is much louder than 40 Decibels.
I'd figure that it would be by 50 meters or something.