A baseball coach shouts loudly at an umpire standing 5.0...

A baseball coach shouts loudly at an umpire standing 5.0 meters away. If the sound power produced by the coach is $3.1 \times 10^{-3} \mathrm{W}$, what is the decibel level of the sound when it reaches the umpire? (Hint: See Sample Problem $13 \mathrm{A}$, then use Table $13-2$ on page 490 .

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Key Concepts

Sound Power

Sound power refers to the total energy per unit time emitted by a sound source, measured in watts. It is an intrinsic property of the source that quantifies how much acoustic energy is being produced, regardless of the medium or distance from the source.

Inverse-Square Law

The inverse-square law describes how sound (or any point-source energy) spreads out in space; as the distance from the source increases, the energy per unit area diminishes proportionally to the square of the distance. This is key for understanding how sound intensity decreases as it propagates away from the source.

Sound Intensity

Sound intensity is a measure of the sound power per unit area, expressed in watts per square meter (W/m²). It is calculated by dividing the sound power by the surface area over which the energy is spread, typically a sphere in free-field conditions, making it directly affected by the inverse-square law.

Decibel Scale

The decibel scale is a logarithmic scale used to express the ratio of a given sound intensity to a reference intensity, usually taken as 1×10?¹² W/m². It compresses a wide range of sound intensities into more manageable numbers, and is calculated using the formula 10 log(I/I?), where I is the measured intensity and I? is the reference intensity.

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