The level of sound V in decibels with an intensity I can be models by V=10log(I/10^-16) where I is intensity watts per centimeter. Loud music can have an intensity of 10^-5 watts per centimeter. Find the level of sound of loud music.
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all you have to do is replace I with 10^-5, then do the arithmetic
V=10log(I/10^-16)
V=10log(10^-5/10^-16)
= 10log(10^11)
= 11(10log 10)
= 11(10)(1) = 110 decibels
To find the level of sound of loud music, we can plug in the intensity value into the given formula V = 10log(I/10^-16).
Given: I = 10^-5 watts per centimeter
Substituting the value of I into the formula:
V = 10log(10^-5/10^-16)
To simplify the expression, we can use the property of logarithms: log(a/b) = log(a) - log(b).
V = 10(log(10^-5) - log(10^-16))
Using the property log(a^b) = b*log(a), we can further simplify:
V = 10(-5 * log(10) - (-16 * log(10)))
Since log(10) equals 1, the expression becomes:
V = 10(-5 - (-16))
Simplifying the exponent:
V = 10(-5 + 16)
V = 10^11
Therefore, the level of sound of loud music is 11 decibels.
To find the level of sound (V) of loud music, we need to substitute the given intensity (I) into the given formula and evaluate it.
Given:
Intensity (I) = 10^-5 watts per centimeter
Formula:
V = 10log(I/10^-16)
Substituting the given intensity into the formula:
V = 10log(10^-5/10^-16)
To simplify the calculation, we can simplify the fraction inside the logarithm:
V = 10log(10^11)
Using the logarithmic property log(b^a) = a * log(b):
V = 10 * 11
Calculating the final answer:
V = 110 decibels
Therefore, the level of sound of loud music is 110 decibels.