Question

Given that I0=10−12 watts/meter2, what is the intensity of a sound for which the decibel level of the sound measures 115? Round off your answer to three decimal places.

Answer 1

To find the intensity of a sound with a decibel level of 115 dB, you use the equation β = 10 log10(I / I0) and solve for I. With the reference intensity I0 being 10−12 W/m², the sound intensity I is calculated to be 0.316 W/m² after rounding to three decimal places.

Step-by-step explanation:

To calculate the intensity of a sound for which the decibel level measures 115 dB, we use the formula for sound intensity level in decibels (dB):

β = 10 log10(I / I0)

where β is the sound intensity level in decibels, I is the sound intensity in watts per meter squared (W/m²), and I0 is the reference intensity, which is 10−12 W/m² - the lowest intensity of sound a person with normal hearing can perceive.

The formula can be rearranged to solve for I, the intensity of the sound:

I = I0 × 10(β/10)

Substitute 115 for β and 10−12 for I0:

I = 10−12 W/m² × 10^(115/10)

I = 10−12 W/m² × 10^11.5

I = 10−0.5 W/m²

I = 0.316 W/m²

After calculating, we find that the sound intensity for a sound measuring 115 dB is approximately 0.316 W/m², rounded off to three decimal places.