Loud vs. Quiet

How loud is a whisper compared with a rock concert? Turn up the speaker's amplitude, walk away from it and watch the decibel meter.

Level at you
70 dB
Sound pressure
63 mPa
Intensity
9.7×10⁻⁶ W/m²
Vs. talking (60 dB)
2.0× louder

The maths, live

Decibels L = 20 × log₁₀(p ÷ p₀), p₀ = 20 µPaL = 20 × log₁₀(63 mPa ÷ 20 µPa) = 70 dB
Distance L = L₁ − 20 × log₁₀(r)L = 70 − 20 × log₁₀(1.0) = 70 dB
+10 dB = 10× intensity ≈ 2× as loud10 dB vs talking: 1.0×10¹× intensity, ≈ 2.0× as loud

Double the distance and the level drops by 6 dB. Loud sounds damage hearing: 85 dB for hours or 120 dB for moments can hurt your ears for good.

How it works

A bigger amplitude means bigger pressure wobbles in the air, and a louder sound. We measure loudness in decibels (dB): L = 20 × log₁₀(p ÷ p₀), where p₀ = 20 µPa is the quietest sound we can hear. A whisper is about 30 dB, talking 60 dB, a busy road 80 dB and a concert 110 dB.

Decibels go up in steps of ten times: every +10 dB means ten times more sound energy (intensity), but to our ears it only sounds about twice as loud. Sound also spreads out as it travels, so each time you double your distance from the speaker the level drops by about 6 dB.

Try this

  1. Press "Add 10 dB". How many times bigger does the intensity get?
  2. Start at 1 m and keep doubling the distance. How much does the level drop each time?
  3. How far away do you need to be from a 110 dB speaker for it to sound like talking?