A certain loudspeaker system emits sound isotropically with...

A certain loudspeaker system emits sound isotropically with a frequency of 2000 $\mathrm{Hz}$ and an intensity of 0.960 $\mathrm{mW} / \mathrm{m}^{2}$ at a distance of 6.10 $\mathrm{m} .$ Assume that there are no reflections. (a) What is the intensity at 30.0 $\mathrm{m} ?$ At $6.10 \mathrm{m},$ what are (b) the displacement amplitude and (c) the pressure amplitude?

A certain loudspeaker system emits sound isotropically with a frequency of 2000 $\mathrm{Hz}$ and an intensity of 0.960 $\mathrm{mW} / \mathrm{m}^{2}$ at a
distance of 6.10 $\mathrm{m} .$ Assume that there are no reflections. (a) What
is the intensity at 30.0 $\mathrm{m} ?$ At $6.10 \mathrm{m},$ what are (b) the displacement amplitude and (c) the pressure amplitude?

Key Concepts

Sound Intensity

Sound intensity is a measure of the power carried by a sound wave per unit area perpendicular to the direction of propagation. It is expressed in watts per square meter and helps us understand how energy is distributed as the wave propagates through a medium. In problems involving point sources that emit sound isotropically, the intensity decreases with distance due to the spreading of the wave over an enlarging spherical surface.

Inverse Square Law

The inverse square law is a fundamental principle that applies to any point source radiating energy equally in all directions. It states that the intensity of the sound is inversely proportional to the square of the distance from the source. This means that as the distance from the source increases, the sound intensity decreases dramatically, which is crucial when calculating intensity at different distances.

Displacement Amplitude

Displacement amplitude refers to the maximum displacement of the particles in the medium from their equilibrium position as a sound wave passes. This concept is important in understanding the physical motion within the medium that results from the passage of a sound wave, and it is related to the energy carried by the wave.

Pressure Amplitude

Pressure amplitude is the measure of the maximum change in pressure from the ambient (or equilibrium) pressure in the medium due to the sound wave. It is directly related to the loudness of the sound and connects to the oscillatory motion of the particles in the medium, relating to the displacement amplitude through the medium's acoustic properties.

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