If a sound source's distance triples, how is the measured energy affected?

If a sound source's distance triples, how is the measured energy affected?

• A. unchanged
• B. 1/4 as intense
• C. 1/9 as intense
• D. 10 percent as intense

Answer: (D)

When considering how distance affects sound energy, it's important to understand the inverse square law, which states that the intensity (or power) of a sound diminishes with the square of the distance from the source. This means that if the distance from the sound source is tripled, the intensity of the sound is not merely reduced linearly, but rather follows the square of that increase in distance. If the original distance is represented as 1 unit, when it is tripled, the new distance becomes 3 units. The intensity at three times the distance can be calculated by squaring the distance ratio (3² = 9). Therefore, the intensity at that distance is 1/9 of the original intensity when compared at the initial distance. Consequently, the correct answer indicates that the sound's measured energy is 1/9 as intense as it was at the original distance. This relationship illustrates the effect of distance on sound propagation and energy distribution in a practical manner.

When considering how distance affects sound energy, it's important to understand the inverse square law, which states that the intensity (or power) of a sound diminishes with the square of the distance from the source. This means that if the distance from the sound source is tripled, the intensity of the sound is not merely reduced linearly, but rather follows the square of that increase in distance.

If the original distance is represented as 1 unit, when it is tripled, the new distance becomes 3 units. The intensity at three times the distance can be calculated by squaring the distance ratio (3² = 9). Therefore, the intensity at that distance is 1/9 of the original intensity when compared at the initial distance.

Consequently, the correct answer indicates that the sound's measured energy is 1/9 as intense as it was at the original distance. This relationship illustrates the effect of distance on sound propagation and energy distribution in a practical manner.