In an idealized physics textbook, waves travel forever and oscillators swing indefinitely. In reality, energy is always lost to friction, air resistance, or absorption. Sound fades with distance. A plucked guitar string eventually goes silent. A pendulum eventually comes to rest.
The MCAT expects you to know why and how these losses happen — and to recognize the three regimes of damping (underdamped, critically damped, overdamped).
Attenuation of Sound
Attenuation is the decrease in sound intensity as a wave travels through a medium. Two main causes:
1. Geometric spreading. As a sound wave radiates outward from a point source, its energy spreads over an ever-larger spherical surface. Surface area = 4πr2, so intensity drops with the square of the distance.
2. Absorption. The medium itself turns sound energy into heat through internal friction between vibrating molecules. Higher frequencies are absorbed faster than lower frequencies — which is why you hear the bass thumping from a distant concert long before you can make out any vocals or high-frequency cymbal hits. Absorption depends on the medium’s properties and on the wave frequency.
Damping in Oscillating Systems
Damping is the loss of energy in an oscillating system due to friction, air resistance, or internal forces. A damped oscillation has shrinking amplitude over time, even though the frequency stays roughly the same (for the underdamped case).
Three regimes the MCAT expects you to know:
Underdamped — the system oscillates with gradually shrinking amplitude. Each swing is slightly smaller than the last. Examples: a pendulum swinging in air, a vibrating guitar string, a car bouncing after hitting a bump.
Critically damped — the system returns to equilibrium as quickly as possible without oscillating. This is the ideal setting for car shock absorbers — you want the car to settle quickly after a bump without bouncing back and forth.
Overdamped — the system returns to equilibrium slowly without oscillating. Like trying to swing a pendulum through honey — it just creeps back to center without ever overshooting.
A speaker produces a sound intensity of 0.01 W/m² at 2 m. What is the intensity at 6 m?
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About 1.1×10−3 W/m². Inverse square: distance tripled → intensity drops by 32=9. I=0.01/9≈0.0011 W/m². Same energy spread over 9× the area.
A pendulum swings in air and gradually comes to rest. Is this system underdamped, critically damped, or overdamped? What happens to its frequency?
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Underdamped. The pendulum oscillates back and forth with shrinking amplitude before stopping. Frequency stays roughly constant throughout the decay. Energy is gradually lost to air resistance and friction at the pivot, turning mechanical energy into heat.
Why do you hear the bass beat from a distant concert long before you can make out the lyrics?
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Higher frequencies are absorbed faster than lower frequencies. Bass (low frequency) is absorbed slowly by air and obstacles, so it carries far. The high-frequency content of vocals and cymbals is absorbed quickly, so it dies off long before the bass does. This is why "thump-thump-thump" is what you hear from a block away — only the bass survives.
