Find the number of decibels for the power of the sound. Round to the nearest decibel.
A rock concert, 5.35 10-6 watts/cm2
D =______ dB
To find the number of decibels (dB) for the power of a sound, you can use the formula:
D = 10 * log10(P/P0)
Where:
- D is the number of decibels
- P is the power of the sound in watts per square centimeter (W/cm^2)
- P0 is the reference power level, which is typically the threshold of hearing (about 10^(-12) W/cm^2).
In this case, the power of the sound at the rock concert is given as 5.35 * 10^(-6) W/cm^2.
To find D, substitute the values into the formula:
D = 10 * log10(5.35 * 10^(-6) / 10^(-12))
Now let's calculate it step by step:
1. First, divide the power of the sound by the reference power level:
5.35 * 10^(-6) / 10^(-12) = 5.35 * 10^(-6+12)
2. Simplify the exponent:
5.35 * 10^(6) = 5.35 * 1,000,000 = 5,350,000
3. Take the logarithm base 10 of the result:
log10(5,350,000) = 6.728
4. Multiply the logarithm by 10:
D = 10 * 6.728 = 67.28 decibels
Rounding to the nearest decibel, the number of decibels for the power of the sound at the rock concert is 67 decibels.