Find the number of decibels for the power of the sound given. Round to the nearest decibel.
A rocket engine, 2.67 cross 10−5watts/cm2
dB = 10Log(2.67*10^-5/10^-16)
= 10Log(2.67*10^11)
= 10(11+Log 2.67)
= 10(11.4265)
= 114 dB
Solution as outlined at
http://www.convert-me.com/en/bb/viewtopic.php?t=699
To find the number of decibels for the power of the sound, you can use the equation:
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 (which is usually set at 10^-12 watts/cm^2).
In this case, the power of the sound is given as 2.67 x 10^-5 watts/cm^2. Therefore, we can substitute these values into the equation:
dB = 10 log10((2.67 x 10^-5) / (10^-12))
Now, let's calculate it step-by-step:
Step 1: Calculate the fraction inside the logarithm:
(2.67 x 10^-5) / (10^-12) = 2.67 x 10^-5 x 10^12 = 2.67 x 10^7
Step 2: Calculate the logarithm:
log10(2.67 x 10^7)
To find the logarithm value, you can use a scientific calculator or an online calculator. For example, log10(2.67 x 10^7) is approximately equal to 7.427.
Step 3: Multiply the logarithm by 10:
dB = 10 x 7.427 = 74.27
Round the value to the nearest decibel:
dB ≈ 74 decibels
Therefore, the number of decibels for the power of the sound is approximately 74 decibels.