Find the number of decibels for the power of the sound given. Round to the nearest decibel.
A rocket engine,
2.42 cross 10−5
watts/cm2
I = 2.42*10^-5 watts/cm^2 = Intensity.
Io = 1*10^-16 watts/cm2 = Reference.
db = 10*Log(I/Io)
db = 10*Log(2.42*10^-5/1*10^-16)
db = 10*Log(2.42*10^11) = 114.
To find the number of decibels for the power of the sound given in watts/cm2, we 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/cm2, and P0 is the reference power level which is generally taken as 10^-12 watts/cm2.
In this case, P = 2.42 * 10^-5 watts/cm2. Plugging this into the formula, we get:
dB = 10 * log10(2.42 * 10^-5 / 10^-12)
First, let's simplify the fraction inside the logarithm:
2.42 * 10^-5 / 10^-12 = 2.42 * 10^-5 * 10^12 = 2.42 * 10^7
Next, we can use a calculator or an online tool to find the logarithm (base 10) of this value. The logarithm of 2.42 * 10^7 is approximately 7.383.
Therefore, dB = 10 * 7.383 = 73.83.
Rounding this to the nearest decibel, the number of decibels for the power of the sound given is approximately 74 decibels.