but this is the last problem, so I'll be done after thins one. :) You're at a concert at a distance of 10m away from the band and their sound level is 120dB. How far back do you have to move if you want the sound level to be 85 dB?
I tried using 85=(10/r1)^2, but this doesn't seem to be working.
To solve this problem, you need to use the inverse square law for sound propagation. According to the inverse square law, the sound intensity decreases as the square of the distance from the source increases.
The formula for the inverse square law is:
I2 = (I1 * (r1^2)) / (r2^2)
Where:
I1 is the initial sound intensity (in this case, 120 dB)
r1 is the initial distance from the source (in this case, 10 m)
I2 is the desired sound intensity (in this case, 85 dB)
r2 is the desired distance from the source (which we need to find)
Let's plug in the values into the formula:
85 = (120 * (10^2)) / (r2^2)
To solve for r2, we can rearrange the equation:
(120 * (10^2)) / 85 = r2^2
(120 * 100) / 85 = r2^2
(12000) / 85 = r2^2
141.18 = r2^2
Now, to find r2, we take the square root of both sides:
r2 = √141.18
r2 ≈ 11.88 m
Therefore, you would need to move back approximately 11.88 meters if you want the sound level to be 85 dB.