Question

Two people are talking at a distance of 3.0 m from where you are, and

you measure the sound intensity as 1.1'10 W/m. Another student
is 4.0 m away from the talkers. Calculate a reasonable estimate for the
sound intensity that the other student measures.
A) 62' 10-8 W/m2
B) 1.5'10-7 W/m2
8.3' 10-8 W/m2
D) 7.8'10-7 W/m2

Answer 1

The sound intensity that the other student measure, I₂ is expected to be;

A) 6.2 × 10⁻⁸ W/m²

Step-by-step explanation:

The measure of sound intensity is given by the following formula;

`I = (P)/(4 \cdot \pi \cdot R^2)`

`(I_2)/(I_1) = (R_1^2)/(R_2^2)`

Where;

I = The intensity

R = The radius

P = The power of the sound

Whereby we have;

The distance of the two people talking, R₁ = 3.0 m

The measure of the sound intensity, I₁ = 1.1 × 10⁻⁷ W/m² (from an online source)

The distance of the other student from the two people talking, R₂ = 4.0 m

Therefore, the estimate of the sound intensity, I₂, is given as follows;

`{I_2} = (R_1^2)/(R_2^2) * {I_1}`

`{I_2} = ((3.0 \, m)^2)/((4.0 \, m)^2) * 1.1 * 10^(-7) \ W/m^2 = 6.1875 * 10^(-8) \ W/m^2`

I₂ = 6.1875 × 10⁻⁸ W/m²

∴ The sound intensity that the other student measure, I₂ ≈ 6.2 × 10⁻⁸ W/m²