Find the number of decibels for the power of the sound given. Round to the nearest decibel.
A rocket engine,
2.37 cross 10−5
watts/cm2
The usual reference level is 10^-12 W/m^2
Here, you have 2.37*10^-5 W/cm^2 = 2.37*10^-1 W/m^2
The dB level is thus
10 log(2.37*10^11) = 10*11.37 = 113.7 dB
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 (which is usually set to 10^-12 watts/cm^2).
In this case, the power of the sound is given as 2.37 x 10^-5 watts/cm^2. We can use P₀ = 10^-12 watts/cm^2 as the reference power level.
Plugging these values into the formula, we get:
dB = 10 * log10((2.37 x 10^-5) / (10^-12))
Now, let's solve this equation step by step:
First, divide the power of the sound by the reference power level:
(2.37 x 10^-5) / (10^-12) = 2.37 x 10^(-5-(-12)) = 2.37 x 10^(-5+12) = 2.37 x 10^7
Next, take the logarithm (base 10) of the result:
log10(2.37 x 10^7) ≈ 7.374
Finally, multiply the result by 10 to get the number of decibels:
dB ≈ 10 * 7.374 ≈ 73.74
Rounded to the nearest decibel, the number of decibels for the power of the sound is approximately 74 dB.