On th decibel scale, the loudness of a sound, in decibels, is given by
D=10log(I/I0), where I is the intensity of a sound barely audible to the human ear. If the intensity of a sound is 10^11I0, what is the loudness in decibels? (please note the I0 is supossed to be I lower 0.
To find the loudness of a sound in decibels using the given formula, we need to substitute the provided values into the equation and calculate the result.
The formula given is: D = 10log(I/I0)
Where:
D = Loudness of the sound in decibels.
I = Intensity of the sound.
I0 = Intensity of a sound barely audible to the human ear.
In this case, the intensity of the sound is given as 10^11I0.
Substituting the values into the formula:
D = 10log((10^11I0)/I0)
To simplify this expression, we can cancel out the I0 terms:
D = 10log(10^11)
Now, we can simplify further by using the logarithmic property log(a^b) = b * log(a):
D = 10 * 11
Finally, we can calculate the result:
D = 110
Therefore, the loudness of the sound is 110 decibels.