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.
Of course it does not work. dB has a special logarithmic meaning, and you need to apply that. Each doubling of the the distance changes the intensity 6db, so you want to have a change of 35db, so your answer ought to be near 6 doublings
10,20, 40, 80, 160, etc.
Use the log formula.
dB x distance^2 = K
120dB x 10^2 = 85dB X d^2
Divide both sides by 85dB
141 = d^2
11.874342087
You should sit 11.87 meters from the band for the sound level to be 85dB.
To solve this question, you can use the inverse square law, which states that the intensity of sound decreases in proportion to the square of the distance from the source. Here's how you can calculate the new distance:
1. Recall that the decibel scale is logarithmic, so the difference between two sound levels is given by the formula:
ΔdB = 10 * log(I₁/I₂)
In this case, we have:
ΔdB = 120 dB - 85 dB = 35 dB
2. Convert the difference in decibels to a ratio of intensities:
10^(ΔdB/10) = I₂/I₁
Plugging in the values:
10^(35/10) = I₂/I₁
10^3.5 = I₂/I₁
3162.27766017 = I₂/I₁
3. Since we want to find the distance at which the sound level is 85 dB, we can equate the ratios of intensities to the ratio of distances squared:
I₂/I₁ = (r₁/r₂)^2
Plugging in I₂/I₁ = 3162.27766017:
3162.27766017 = (10/r₂)^2
4. Solve for r₂:
3162.27766017 = 100/r₂^2
Taking the square root of both sides:
sqrt(3162.27766017) = 10/r₂
r₂ = 10/sqrt(3162.27766017)
r₂ ≈ 0.316 meters
So, if you want the sound level to be 85 dB, you would need to move approximately 0.316 meters (or 31.6 centimeters) away from the band.