The power of a point source of sound and the distance at...

The power of a point source of sound and the distance at which the sound is heard are given below for four different cases. Rank cases A through D in order of increasing intensity. Indicate ties where appropriate. Case A: $P=10 \mathrm{~W}, r=1 \mathrm{~m}$ Case B: $P=20 \mathrm{~W}, r=2 \mathrm{~m}$ Case C: $P=50 \mathrm{~W}, r=5 \mathrm{~m}$ Case D: $P=100 \mathrm{~W}, r=5 \mathrm{~m}$

The power of a point source of sound and the distance at which the sound is heard are given below for four different cases. Rank cases A through D in order of increasing intensity. Indicate ties where appropriate.
Case A: $P=10 \mathrm{~W}, r=1 \mathrm{~m}$
Case B: $P=20 \mathrm{~W}, r=2 \mathrm{~m}$
Case C: $P=50 \mathrm{~W}, r=5 \mathrm{~m}$
Case D: $P=100 \mathrm{~W}, r=5 \mathrm{~m}$

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Key Concepts

Effect of Distance on Intensity

As distance increases, the intensity of sound decreases because the same amount of power is distributed over a larger area. This concept is crucial for comparing different scenarios where both the power of the source and the distance from it vary.

Source Power

The power of the sound source directly affects the sound intensity. A source with a higher power emits more energy, which in turn produces a higher intensity at a given distance compared to a source of lower power, assuming identical conditions for distribution.

Sound Intensity

Sound intensity is defined as the power per unit area carried by a sound wave. It is typically calculated using the formula I = P / (4?r²) for a point source emitting sound uniformly in all directions, where P is the power of the sound source and r is the distance from the source.

Inverse Square Law

The inverse square law describes how the intensity of a sound decreases with distance. Because the sound energy spreads out over the surface area of a sphere, which increases as 4?r², the intensity falls off proportionally to the square of the distance from the source.

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