Sound Intensity and Decibels

The human ear is staggeringly sensitive. It can detect sound waves with intensities as low as $10^{-12}$ W/m² (literally a mosquito flying across a quiet room) — and it can tolerate sounds a trillion times more intense before reaching the pain threshold.

Because that range is so enormous, plain intensity numbers (in W/m²) become unwieldy fast. So we use a logarithmic scale — decibels (dB) — that compresses the trillion-fold range into a manageable 0–120. The MCAT loves decibels because they teach you how logarithms compress huge ranges, and because they show up in passages on hearing, music, hearing loss, and noise pollution.

Sound Intensity

Intensity is the power delivered per unit area, measured in W/m².

The Decibel Scale

Because intensity spans 12 orders of magnitude between the faintest audible sound and the pain threshold, we use a logarithmic compression:

The Key dB Shortcuts

You don’t need a calculator for MCAT decibel problems. These three rules cover almost every question:

Going the other direction:

• Every +10 dB → 10× more intense.
• Every +20 dB → 100× more intense.
• Every +30 dB → 1000× more intense.

Common Sound Levels

Hearing damage starts to happen with prolonged exposure above about 85 dB — which is why sustained exposure to loud music, lawnmowers, or industrial noise can cause permanent hearing loss over time.

Worked Example

A siren produces a sound level of 90 dB at 10 m away. What’s the sound level at 100 m?

1. Distance grows by 10× (from 10 m to 100 m).
2. Intensity follows inverse square: $I$ drops by $10^2 = 100$.
3. dB change: $10 \log(1/100) = 10 \times (-2) = -20$ dB.
4. New level: $90 - 20 = 70$ dB.

So a siren that’s painfully loud right next to you (90 dB) drops to “loud TV” level (70 dB) just 100 m away. This is why ambulances need to be very loud at the source — they’re projecting outward from a point.