find the number of decibels for for the power of the sound given. Round to the nearest decibel. a rocket engine, 2.4 X 10 -5 watts/cm2
10 log (2.4*10^-5/10^-16)
10 [ log 2.4 + log 10^11]
10 [11+.38] = 114
To find the number of decibels (dB) for the power of a sound, you can use the following formula:
dB = 10 * log10(P / P0)
Where:
- dB is the number of decibels
- P is the power of the sound in watts/cm^2
- P0 is the reference power, usually set at the threshold of human hearing, which is approximately 1 x 10^(-12) watts/cm^2
Using the given power of the sound as 2.4 x 10^(-5) watts/cm^2, we can substitute the values into the formula:
dB = 10 * log10(2.4 x 10^(-5) / 1 x 10^(-12))
Simplifying this expression, we have:
dB = 10 * log10(2.4 x 10^7)
Now we can calculate the number of decibels using a calculator or by hand:
dB ≈ 10 * log10(24,000,000)
dB ≈ 10 * 7.38
dB ≈ 73.8
Therefore, the number of decibels for a rocket engine with a power of 2.4 x 10^(-5) watts/cm^2 is approximately 73.8 dB (rounded to the nearest decibel).
To find the number of decibels for a given power of sound, you can use the formula:
Decibels = 10 * log10(Power / Reference)
Where:
- Power is the given power of the sound in watts/cm²
- Reference is the reference power level, typically 10^(-12) watts/cm²
Using the given power of the sound as 2.4 x 10^(-5) watts/cm², we can calculate the number of decibels as follows:
Decibels = 10 * log10(2.4 x 10^(-5) / 10^(-12))
Decibels = 10 * log10(2.4 x 10^7)
Decibels = 10 * log10(24,000,000)
Calculating this using a calculator or math software, we get:
Decibels ≈ 73.979
Rounding to the nearest decibel, the number of decibels for a rocket engine with a power of 2.4 x 10^(-5) watts/cm² is approximately 74 decibels.