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.