Find the number of decibels for the power of the sound. Round to the nearest decibel.

A rock concert, 5.21 multiplied by 10-6 watts/cm2

5.21=-6

To find the number of decibels for the power of the sound, we need to use the formula:

dB = 10 * log10(P1/P0)

Where P1 is the power of the sound and P0 is the reference power level, which is typically set at 10^-12 watts/cm^2 for sound.

In this case, P1 is given as 5.21 * 10^-6 watts/cm^2.

So plugging these values into the formula:

dB = 10 * log10( (5.21 * 10^-6) / (10^-12) )

To evaluate this expression, we can simplify the division inside the logarithm:

dB = 10 * log10( (5.21 * 10^6) / 1 )

dB = 10 * log10( 5.21 * 10^6 )

Now, let's calculate the value inside the logarithm:

log10( 5.21 * 10^6 ) = log10( 5.21 ) + log10( 10^6 )

Since log10(10^6) = 6, the expression simplifies to:

log10( 5.21 * 10^6 ) = log10( 5.21 ) + 6

Using a scientific calculator or a logarithm table, we can find that:

log10( 5.21 ) ≈ 0.716

Now, let's substitute this value back into the original equation:

dB = 10 * (0.716 + 6)

dB = 10 * 6.716

dB ≈ 67.16

Rounding to the nearest decibel, the number of decibels for the power of the sound is approximately 67 dB.