Question

The sound intensity level of a jet plane going down the runway as observed from a certain location is 105 dB. What is the intensity of the sound at this location?

A) 10^-10 W/m²
B) 10⁻9 W/m²
C) 10⁻8 W/m²
D) 10⁻7 W/m²

Answer 1

The intensity of a sound at a certain location with a sound intensity level of 105 dB is 10^-7 W/m², which corresponds to option D.

Step-by-step explanation:

To determine the intensity of sound at a certain location with a sound intensity level of 105 dB, we use the formula relating intensity in watts per meter squared (W/m²) to the decibel level (dB):

L = 10 · log10(I/I0)

where L is the sound intensity level in decibels, I is the intensity of the sound, and I0 is the reference intensity of 10⁻¹² W/m² (the threshold of hearing).

Rearranging the formula to solve for I gives:

I = I0 · 10^(L/10)

For a sound intensity level of 105 dB, substituting the known values:

I = 10⁻¹² W/m² · 10^(105/10)

I = 10⁻¹² W/m² · 10^10.5

I = 10⁻ⁱ W/m²

So, the intensity of the sound at this location is 10⁻⁷ W/m², which corresponds to option D.