Find the number of decibels for the power of the sound. Round to nearest decibels.
A rock concert, 5.21 x 10^-6watts/cm^2
D= dB
To find the number of decibels (dB) for the power of sound, you can use the formula:
dB = 10 * log10(P/P0)
Where:
- dB 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, usually set at 10^(-12) watts per square centimeter (W/cm^2)
Given that the power of the sound at the rock concert is 5.21 x 10^(-6) watts/cm^2, we can now calculate the number of decibels:
dB = 10 * log10(5.21 x 10^(-6))/(10^(-12))
Using a scientific calculator, we can calculate the logarithm term:
log10(5.21 x 10^(-6)) = -5.283
Now, we can substitute this value back into the formula:
dB = 10 * (-5.283)/(10^(-12))
Using the order of operations (PEMDAS/BODMAS), perform the calculations inside the parentheses first:
dB = -52.83/(10^(-12))
Next, calculate 10 to the power of -12:
10^(-12) = 0.000000000001
Substitute this value back into the equation:
dB = -52.83/0.000000000001
Divide -52.83 by 0.000000000001:
dB = -52,830,000,000
Finally, round this value to the nearest decibel:
dB ≈ -52,830,000,000 (rounded to the nearest decibel)
Therefore, the number of decibels for the power of sound at the rock concert is approximately -52,830,000,000 dB.