Find the number of decibels for the power of the sound given. Round to the nearest decibel.
A rocket engine,
2.32 cross product 10−5
watts/cm2
To find the number of decibels for the power of the sound, we can use the formula:
dB = 10 * log10(P2/P1)
Where P2 is the power of the sound in question, and P1 is a reference power (usually taken as the threshold of hearing, which is 10^−12 watts/cm^2).
In this case, the power of the sound given is 2.32 * 10^−5 watts/cm^2. To find the number of decibels, we need to calculate the ratio of the given power to the reference power and then take the logarithm (base 10) of that ratio.
First, calculate the ratio:
P_ratio = P2/P1 = (2.32 * 10^−5) / (10^−12) = 2.32 * 10^7
Next, take the logarithm of the ratio:
dB = 10 * log10(2.32 * 10^7)
Using a scientific calculator or a calculator with a logarithm function, calculate the logarithm and multiply by 10:
dB = 10 * (log10(2.32) + log10(10^7))
= 10 * (0.3665 + 7)
= 10 * 7.3665
= 73.665
Finally, round the result to the nearest decibel:
The number of decibels for the power of the sound given is approximately 74 decibels.