Question

The low-frequency speaker of a stereo set has a surface area of 0.05 m² and produces 1 W of acoustical power. What is the intensity at the speaker? If the speaker projects sound uniformly in all directions, at what distance from the speaker is the intensity 0.1 W/m²?

a) 20 W/m², 10 m
b) 2 W/m², 1 m
c) 40 W/m², 5 m
d) 10 W/m², 2 m

Answer 1

The intensity at the speaker is 20 W/m². The distance from the speaker where the intensity is 0.1 W/m² is 10 m.

Step-by-step explanation:

The intensity at the speaker can be calculated using the formula:

Intensity = Power / Area

Substituting the given values, we have:

Intensity = 1 W / 0.05 m² = 20 W/m²

To find the distance at which the intensity is 0.1 W/m², we can use the inverse square law:

Intensity1 / Intensity2 = (Distance2 / Distance1)²

Substituting the given values, we have:

(20 W/m²) / (0.1 W/m²) = (Distance2)² / (Distance1)²

Simplifying the equation, we find:

Distance2 = sqrt((20 W/m²) / (0.1 W/m²))

Distance2 = 10 m