Find the number of decibels for the power of the sound given. Round to the nearest decibel.A rocket engine, 2.42 * 10^−5 watts/cm2
dB = 10log(2.42*10^-5 / 10^-16)
= 10log(2.42*10^11)
= 113.8 dB
To find the number of decibels for the given power of sound, we can use the formula:
Decibels = 10 * log10(Power / Reference)
Where the reference is usually taken as 10^−12 watts/cm^2.
Let's calculate the number of decibels for the given power:
Decibels = 10 * log10(2.42 * 10^−5 / 10^−12)
Decibels = 10 * log10(2.42 * 10^7)
Decibels = 10 * 7.384
Decibels ≈ 73.84 (rounded to the nearest decibel)
Therefore, the number of decibels for a rocket engine with a power of 2.42 * 10^−5 watts/cm^2 is approximately 73.84 decibels.
To find the number of decibels for the power of the 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, and P0 is the reference power level (usually 10^−12 watts/cm^2).
In this case, the power of the sound is 2.42 * 10^−5 watts/cm^2.
Using the formula, we can calculate the number of decibels:
dB = 10 * log10(2.42 * 10^−5 / 10^−12)
Simplifying the calculation within the logarithm:
dB = 10 * log10(2.42 * 10^7)
Now, calculate the logarithm:
dB = 10 * 7.3847
Finally, calculate the number of decibels:
dB ≈ 73.847
Rounding to the nearest decibel:
dB ≈ 74 decibels
Therefore, the number of decibels for the power of the sound of a rocket engine with a power of 2.42 * 10^−5 watts/cm^2 is approximately 74 decibels.