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 cm^2
what is the db?
db=10*Log(2.42*10^5)=10*Log(242000) = 54
Correction:
db = 10*Log(2.42*10^5/10^-16) =
10*Log(2.42*10^21) = 81
Oops!!
10*Log(2.42*10^21) = 214 db.
To find the number of decibels (dB) for the power of the sound, we can use the formula:
dB = 10 * log10(P/P0)
Where:
- dB is the number of decibels
- P is the power of the sound in watts per square centimeter (W/cm^2)
- P0 is the reference power level, which is 1 W/cm^2
In this case, the power of the sound is given as 2.42 * 10^5 W/cm^2. We can substitute these values into the formula:
dB = 10 * log10(2.42 * 10^5 / 1)
Now, let's evaluate this expression step by step:
1. Calculate the division inside the logarithm:
2.42 * 10^5 / 1 = 2.42 * 10^5
2. Take the logarithm (base 10) of the result:
log10(2.42 * 10^5) = 5.384
3. Multiply the logarithm by 10:
10 * 5.384 = 53.84
Finally, we round the result to the nearest decibel, which gives us approximately 54 dB.