Question

The loudness of a sound, L, in decibels, is related to the relative intensity of the sound, R, by the function L = 10 log R. What is the relative intensity of a sound that has a loudness of 85 decibels?​

Answer 1

177.83

Explanation:

To find the relative intensity (R) of a sound given its loudness (L) in decibels, we can rearrange the equation L = 10 log R to solve for R.

Start with the equation: L = 10 log R

Divide both sides of the equation by 10: L/10 = log R

Take the antilog (inverse logarithm) of both sides, using base 10: 10^(L/10) = R

Now, substitute the given loudness value L = 85 into the equation to find the relative intensity:

R = 10^(85/10)

Using a calculator, evaluate the expression:

R ≈ 177.82794

Therefore, the relative intensity of the sound with a loudness of 85 decibels is approximately 177.83.