A loudspeaker emits sound uniformly in all directions with a power output of 1715.8 watts. What is the sound intensity at a distance of 5.3 meters from the loudspeaker?

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BlackTom AI · Accepted Answer

To determine the sound intensity at a distance from a point source, use the formula I = P / (4πr^2), where P is the power output and r is the distance.
First, compute the square of the distance: r^2 = (5.3 m)^2 = 28.09 m^2.
Next, evaluate the surface area factor for a sphere of radius r: 4πr^2 = 4 × π × 28.09 ≈ 4 × 3.14159 × 28.09 ≈ 353.0 (in units of m^2).
Then substitute into the intensity formula: I = 1715.8 W / 353.0 m^2 ≈ 4.86 W/m^2.
Rounding to appropriate significant figures based on the given data, this value is about 4.9 W/m^2.
Key conceptual point: intensity decreases with the surface area of the sphere over which the power is spread; as distance increases, the area increases as r^2, causing the intensity to fall off accordingly.
Common missteps to avoid include treating intensity as proportional to distance or using incorrect geometric factors (for example, using a planar area instead of the spherical surface area).

MUF0122 Physics Unit 2 - Semester 2, 2025

A loudspeaker emits sound uniformly in all directions with a power output of 1715.8 watts. What is the sound intensity at a distance of 5.3 meters from the loudspeaker?

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