Question

What is the intensity in watts per meter squared of 85.0-dB sound?

a) (1.00 X 10⁻7W/m²)
b) (2.00 X 10⁻7W/m²)
c) (5.00 X 10⁻8W/m²)
d) (1.00 X 10⁻8W/m²)

Answer 1

The intensity of an 85.0-dB sound is calculated using the formula relating intensity to decibels. None of the provided options match the correct calculation, which suggests there may be an error in the question's details.

Step-by-step explanation:

To calculate the intensity (I) in watts per meter squared of a sound with a given decibel level (dB), we use the formula that relates intensity to decibels:

I = I0 * 10(dB/10)

where I0 is the reference intensity threshold for hearing, which is commonly accepted as 1.00 x 10-12 W/m2. Inserting the given value of 85.0 dB:

I = 1.00 x 10-12 W/m2 * 10(85.0/10)

By performing the calculations:

I = 1.00 x 10-12 W/m2 * 108.5

I = 1.00 x 10-12 W/m2 * 3.16227766 x 108

I ≈ 3.16 x 10-4 W/m2

To find the closest answer from the provided options, we need to convert this result into the corresponding scientific notation with two significant figures:

I ≈ 3.16 x 10-4 W/m2 ≈ 3.2 x 10-4 W/m2

However, since none of the provided options match this result, there seems to be an error in the options given. Please cross-check the question details and provided options.