Find the number of decibels for the power of the sound. Round to the nearest decibel.
A rock concert, 5.36 multiplied by 10-6 watts/cm2
D = mark dB
To find the number of decibels 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, and P0 is the reference power level (typically set to the threshold of human hearing, which is 10^-12 watts/cm^2).
In this case, you're given that the power of the sound at a rock concert is 5.36 x 10^-6 watts/cm^2. To find the number of decibels, substitute these values into the formula:
D = 10 * log10((5.36 x 10^-6) / (10^-12)).
First, divide the power of the sound by the reference power level:
D = 10 * log10(5.36 x 10^-6 / 10^-12).
Next, calculate the division:
D = 10 * log10(5.36 x 10^6).
Now, evaluate the logarithm:
D = 10 * log10(5.36) + 10 * log10(10^6).
Using the logarithm properties, we know that log10(10^6) is simply 6, so:
D = 10 * log10(5.36) + 10 * 6.
Calculate the logarithm and multiply by 10:
D ≈ 10 * 0.729 + 60.
D ≈ 7.29 + 60.
D ≈ 67.29.
Since we need to round to the nearest decibel, the number of decibels for the power of the sound at the rock concert is approximately 67 decibels.