Given that I_w = 10^(-12) watts/meter^2, what is the intensity of a sound for which the decibel level of the sound measures 129? Round your answer to four decimal places and remember that L_dB = 10 * log10(I/I_w).
To solve this problem, we need to use the formula for the decibel level (L_dB) in terms of the intensity (I) of the sound and the reference intensity (I_w):
L_dB = 10 * log10(I/I_w)
We are given that the decibel level is 129, so we can plug that into the formula:
129 = 10 * log10(I/10^(-12))
Now, we need to solve for the intensity (I). First, we can divide both sides of the equation by 10:
12.9 = log10(I/10^(-12))
Next, we can rewrite the equation in exponential form:
10^12.9 = I/10^(-12)
Now, we can multiply both sides by 10^(-12) to isolate I:
I = 10^12.9 * 10^(-12)
I = 10^(12.9 - 12)
I = 10^0.9
Now, we can calculate the intensity (I) to four decimal places:
I ≈ 7.9433 watts/meter^2
So, the intensity of the sound is approximately 7.9433 watts/meter^2.