a construction explosion has an intensity i of 1.25 × 10-^4 W/m^2. find the loudness of the sound in decibels if L=10log1/1o and 1o =10-^12 W/m^2. Round to nearest tenth.
We can calculate the loudness of the sound in decibels using the formula L = 10 log10(I/Io), where I is the intensity of the sound and Io is the reference intensity.
Given:
I = 1.25 × 10^(-4) W/m^2
Io = 10^(-12) W/m^2
Using the formula, we can substitute the given values:
L = 10 log10(1.25 × 10^(-4) / 10^(-12))
Simplifying the expression inside the logarithm:
L = 10 log10(1.25 × 10^8)
Now, convert the number inside the logarithm to scientific notation:
L = 10 log10(1.25 × (10^8))
L = 10 log10(1.25) + 10 log10(10^8)
Since log10(10^8) = 8, this simplifies to:
L = 10 log10(1.25) + 8
Using a calculator, find the logarithm of 1.25:
L ≈ 10 × 0.097 + 8
L ≈ 0.97 + 8
L ≈ 8.97
Rounding to the nearest tenth:
L ≈ 9.0
Therefore, the loudness of the sound in decibels is approximately 9.0 decibels.