A rock concert, 5.17 10-6 watts/cm2
D = dB
If the sound intensity is 5.17*10^-6 W/cm^2, the dB level is
10Log(10)[5.17*10^-6/10^-16]
10Log(10)[5.17*10^10] = 107.1 dB
Ref:
http://hyperphysics.phy-astr.gsu.edu/hbase/sound/intens.html#c1
To calculate the sound intensity level in decibels (dB) from the given sound intensity in watts per square centimeter (W/cm²), you can use the following formula:
D = 10 * log10(I/I₀)
Where:
D is the sound intensity level in decibels (dB)
I is the sound intensity in watts per square centimeter (W/cm²)
I₀ is the reference sound intensity, which is typically taken as the threshold of human hearing, or 1.0 x 10⁻¹² W/cm².
So, to find the sound intensity level (D) in decibels for a rock concert with a sound intensity of 5.17 x 10⁻⁶ W/cm², we can substitute these values into the formula:
D = 10 * log10(5.17 x 10⁻⁶ / 1.0 x 10⁻¹²)
Now, let's calculate it step by step:
D = 10 * log10(5.17 x 10⁻⁶ / 1.0 x 10⁻¹²)
D = 10 * log10(5.17 x 10⁻⁶) - log10(1.0 x 10⁻¹²)
Using the properties of logarithms, we can simplify this further:
D = 10 * (log10(5.17) + log10(10⁻⁶)) - (log10(1.0) + log10(10⁻¹²))
D = 10 * (log10(5.17) - 6) - (0 + (-12))
D = 10 * (log10(5.17) - 6) + 12
Now, we can use a logarithmic table or a calculator to find the log10(5.17) term:
D = 10 * (0.712 - 6) + 12
D = 10 * (-5.288) + 12
D = -52.88 + 12
D = -40.88
Therefore, the sound intensity level (D) of the rock concert with a sound intensity of 5.17 x 10⁻⁶ W/cm² is approximately -40.88 dB.