If the distance from a sound source is doubled, what happens to the intensity?

If the distance from a sound source is doubled, what happens to the intensity?

• A. One-fourth
• B. Doubles
• C. Halves
• D. Quadruples

Answer: (A)

The key idea here is how sound energy spreads as you move away from a source. For a point source, the energy radiates outward onto a sphere whose surface area grows with the square of the distance (area ∝ r^2). When you double the distance, the surface area becomes four times larger. Since the same amount of energy is now distributed over a surface four times bigger, the energy per unit area—the intensity—drops by a factor of four. So the new intensity is one-fourth of the original.

The key idea here is how sound energy spreads as you move away from a source. For a point source, the energy radiates outward onto a sphere whose surface area grows with the square of the distance (area ∝ r^2). When you double the distance, the surface area becomes four times larger. Since the same amount of energy is now distributed over a surface four times bigger, the energy per unit area—the intensity—drops by a factor of four. So the new intensity is one-fourth of the original.