At a rock concert, a dB meter registered 130 dB when placed...

At a rock concert, a dB meter registered $130 \mathrm{~dB}$ when placed $2.2 \mathrm{~m}$ in front of a loudspeaker on the stage. $(a)$ What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air? (b) How far away would the sound level be a somewhat reasonable $85 \mathrm{~dB} ?$

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Key Concepts

Decibel Scale

The decibel (dB) scale is a logarithmic measure used to describe sound intensity levels relative to a reference intensity, typically 10?¹² W/m². It converts a wide range of sound intensities into a manageable scale, making it easier to compare widely varying sound energies, and it involves the formula L = 10 log??(I/I?).

Sound Intensity and Power Relationship

Sound intensity is defined as the power per unit area carried by a sound wave. In the context of omnidirectional sound emission, the intensity at a distance r from a point source is given by I = P/(4?r²), where P is the total acoustic power output of the source.

Inverse Square Law in Acoustics

The inverse square law states that for a point source emitting sound uniformly in all directions, the sound intensity decreases in proportion to the square of the distance from the source. This principle underlies the calculations connecting measured decibel levels, distances, and total power output.

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