Find the number of decibels for the power of the sound given. Round to the nearest decibel.
A rocket engine, 2.65 times 10^-5 watts/cm^2
That sound level must correspond to a certain distance from the rocket. You don't say what it is. Sound level increases as you get closer.
Use the definition of decibels.
dB = 10 * log(I/1.0 x 10^-12 W/m^2)
I = 2.65*10^-5 W/cm^2 = 2.65*10^-1 W/m^2
dB = 10*log(0.265/10^-12)
= 10*11.42
= 114 dB
Some rock concerts are louder than that, within the areana.
Thank you for help.
To find the number of decibels (dB) for the power of the sound, you need to use the formula:
dB = 10 * log10(power/reference)
Where power is the given power in watts per centimeter squared (W/cm^2), and the reference is usually taken as the threshold of human hearing, which is 10^-12 watts per square centimeter (W/cm^2).
Let's calculate the number of decibels for the given power:
dB = 10 * log10(2.65 * 10^-5 / 10^-12)
= 10 * log10(2.65 * 10^7)
Now, let's evaluate the expression:
dB = 10 * log10(2.65 * 10^7)
= 10 * log10(2.65) + 10 * log10(10^7)
≈ 10 * 0.423 + 10 * 7
≈ 4.23 + 70
≈ 74.23
Rounding to the nearest decibel, the number of decibels for the power of the sound is approximately 74 dB.