- #1
late347
- 301
- 15
Homework Statement
Intensity of sound is (W/m^2) and is inversely proportional to the the square of the distance measured from the sound source. The noise level of a risiing jet aircraft at the distance of 30m, is 140 dB.
How far from the jet aircraft is the noise level at the level of 120 dB (which is about the noise of rock concert)
Homework Equations
there were no equations provided, and this was from a math textbook. I think the this is the entire problem statement for the specific textbook problem.
I was wondereing how it could be solved with only the information in the problem statement.
However in an earlier problem in the same textbook there was a formula for noise level (L, which has decibels) I'm not 100% certain that is the right word to use in English for the quantity, which is measured in decibels.
L = 120 + 10 lg(I) where I is the sound's intensity.
certainly it seems the problem was solvable if you used that formula. You have to put it in the form of I= something.
The Attempt at a Solution
we know essentially that there is inverse relationship therefore k = constant which we can calculate initially using that L= whatever fromula
## k= I*r^2 \nonumber \\
\leftrightarrow ~~k=10^{\frac{140-120}{10}}*30^2 \nonumber \\
\leftrightarrow ~~k=10^2*30^2 =90000##
from earlier problem's formula we can get an idea what L = noise level (?) will be and what Intensity will be
## L= 120 +10lg(I) \nonumber \\
\leftrightarrow ~~ I= 10^{\frac{L-120}{10}} \nonumber ##
original formula can be used and intensity can be plugged into that original formula
## r^2= \frac{k}{I} \nonumber \\
\leftrightarrow ~~r^2=\frac{90000}{10^{\frac{L-120}{10}}} \nonumber \\
\leftrightarrow ~~r^2=\frac{90000}{10^{\frac{120dB-120dB}{10}}} \nonumber \\
\leftrightarrow ~~r^2=\frac{90000}{1} \nonumber \\
\leftrightarrow ~~r=300##
I was wondering if there is alternative way to do it.