Question

Given that I0=10−12

watts/meter2, what is the intensity of a sound for which the decibel level of the sound measures 141
? Round off your answer to three decimal places.

Answer 1

The intensity of a sound can be calculated using the formula β = 10 log(I/I0), where β is the decibel level, I is the intensity of the sound, and I0 is the reference intensity. Substituting the given values, the intensity of the sound is approximately 0.032 watts per meter squared.

Step-by-step explanation:

The intensity of a sound can be calculated using the formula:

β = 10 log(I/I0)

Where β is the decibel level, I is the intensity of the sound, and I0 is the reference intensity. In this case, I0 is given as 10-12 watts/meter2 and β is given as 141 decibels. We can rearrange the formula to solve for I:

I = I0 * 10^(β/10)

Substituting the given values, we get:

I = (10-12 W/m2) * 10^(141/10)

= 3.162 * 10-2 W/m2