find the number of decibels for the power of the sound. round to nearest decibel.
a rock concert
5.34*10^-6 watts/cm^2
D= Db
To find the number of decibels (Db) for the power of a sound, you can use the formula:
Db = 10 * log10(P/Pref)
Where P is the power of the sound in watts per square centimeter (W/cm^2) and Pref is the reference power level, typically taken to be 10^-12 W/cm^2.
In this case, the power of the sound at a rock concert is given as 5.34 * 10^-6 W/cm^2.
To convert this value to decibels, substitute the given values into the formula:
Db = 10 * log10(5.34 * 10^-6 / 10^-12)
First, simplify the numerator and denominator:
Db = 10 * log10(5.34 * 10^6 / 10^-12)
Next, apply the logarithmic property log(a/b) = log(a) - log(b):
Db = 10 * (log10(5.34 * 10^6) - log10(10^-12))
Evaluate the logarithms:
Db = 10 * (log10(5.34) + log10(10^6) - (-12))
Since log10(10^6) = 6 and -(-12) = 12:
Db = 10 * (log10(5.34) + 6 + 12)
Simplify further:
Db = 10 * (0.727 + 6 + 12)
Db = 10 * 18.727
Db ≈ 187 (rounded to the nearest decibel)
Therefore, the number of decibels for the power of the sound at a rock concert is approximately 187 dB.