Loudness, Decibels and Noise Hazards

How loud is too loud?

After a hockey game, a concert or an afternoon with a leaf blower, your ears may ring. That ringing is a warning: tiny hair cells in your cochlea have been stressed, and if it happens often enough, some will die. They never grow back. In this lesson you will learn how sound strength is measured, why distance helps so much, and how engineers and governments protect people and wildlife from harmful waves.

Sound intensity

Intensity is the sound power passing through each square metre: I = P/A, measured in W/m².

A small source in open air spreads its power over a sphere that grows as the sound moves outward. The surface area of a sphere is 4πr², so

I = P / (4πr²), which means I ∝ 1/r²

This is the inverse square law. Double your distance from a source and the intensity drops to ¼. Triple it and it drops to 1/9. That is why stepping back from a speaker helps a lot. (Indoors, reflections from walls mean the drop is usually smaller.)

The decibel scale

Our ears can handle a huge range: the loudest sound you can bear is about a trillion (10¹²) times as intense as the faintest you can hear. To make these numbers manageable we use the decibel (dB) scale, named after Alexander Graham Bell.

• 0 dB is the threshold of hearing, I₀ = 1 × 10⁻¹² W/m².
• Every +10 dB multiplies the intensity by 10. +20 dB is ×100, +30 dB is ×1000.
• +3 dB is about double the intensity; −3 dB is about half.
• Doubling your distance from a point source (intensity ÷ 4) lowers the level by about 6 dB.

Our ears do not hear intensity directly. As a rough rule, a sound must be about 10 dB higher to seem twice as loud. Noise limits use dBA, a weighted reading that matches how sensitive our ears are at different frequencies.

Noise hazards

Hearing loss. Noise-induced hearing loss is permanent but preventable. In Ontario, the workplace noise regulation sets a limit of 85 dBA averaged over an 8-hour workday. Ontario uses a 3 dB exchange rate: every 3 dB louder halves the safe time (88 dBA: 4 h; 91 dBA: 2 h; 94 dBA: 1 h, and so on). Earbuds turned up high can exceed 100 dB. A common guideline is to keep the volume at or below about 60% and take breaks.

Health and the environment. Long-term traffic and aircraft noise can disturb sleep and raise stress. Animals are affected too: underwater noise from ships can mask the calls that whales use to communicate and find food. In British Columbia, for example, ships have been asked to slow down in some areas to reduce noise near endangered killer whales.

Large mechanical waves. Not all hazardous waves are sound. A tsunami is a series of ocean waves, usually triggered by an undersea earthquake. In the deep ocean its speed is about v = √(g d), where d is the depth and g = 9.8 m/s². In 4000 m of water that is about 200 m/s (over 700 km/h), yet the wave may be less than a metre high. Near shore it slows down, its wavelength shrinks, and its height grows enormously.

Reducing the harm: technologies to assess

• Hearing protection: earplugs and earmuffs absorb sound and can reduce levels reaching the ear by roughly 15 dB to 30 dB, depending on the product and how well it fits.
• Mufflers: a car muffler sends exhaust through chambers and tubes. Some sound is absorbed by packing material, and some is reflected so that it meets incoming sound half a cycle out of phase and interferes destructively.
• Noise barriers: walls beside highways such as the 401 reflect and absorb traffic noise. They work best when they block the line of sight between the road and the homes; some sound still bends (diffracts) over the top, so they reduce noise rather than eliminate it.
• Building design: double-pane windows, insulation and heavy, sealed walls block sound.
• Tsunami warning systems: seismometers detect undersea earthquakes, and seafloor pressure sensors and buoys detect the tsunami itself. Ocean Networks Canada operates seafloor sensors off the coast of British Columbia that contribute to tsunami detection. Early warnings give coastal communities time to move to higher ground.

When you assess a technology, ask: How much does it reduce the hazard? What does it cost? Who benefits and who pays? Does it create new problems? Are there cheaper or simpler alternatives (like reducing the noise at its source)?