Assume a loudspeaker broadcasts sound equally in all...

Assume a loudspeaker broadcasts sound equally in all directions and produces sound with a level of 103 $\mathrm{dB}$ at all distance of 1.60 $\mathrm{m}$ from its center. (a) Find its sound power output. (b) If a salesperson claims to be giving you 150 $\mathrm{W}$ per channel, he is referring to the electrical power input to the speaker. Find the efficiency of the speaker, that is, the fraction of input power that is converted into useful output power.

Key Concepts

Energy Conversion Efficiency

Efficiency in this context refers to the ratio of the useful acoustic power output from the speaker to the electrical power input. This concept is critical in evaluating the performance of audio devices, as it determines how effectively electrical energy is converted into sound energy.

Sound Power Calculation

Sound power is the total acoustic energy emitted by a source per unit time. It can be calculated by multiplying the intensity of sound at a given distance by the surface area of the sphere (with radius equal to that distance) over which the sound is distributed. This approach allows one to relate measurements of sound level at a specific distance to the source's total sound output.

Sound Level Measurement

This concept involves understanding that sound level is expressed in decibels (dB), which is a logarithmic measure of the sound intensity relative to a reference level. The decibel scale compresses a large range of values into a manageable scale and is commonly used to compare sound intensities in acoustics.

Sound Intensity and the Inverse Square Law

Sound intensity is defined as the sound power per unit area, and for sources that radiate uniformly in all directions, the intensity decreases with the square of the distance from the source. This inverse square law is crucial in acoustics for determining how the energy spreads out over an increasing spherical surface area as the distance from the source increases.

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