Loudness perception

# 42 Decibels and sound levels

### Sound Levels

Sounds humans can tolerate sounds that have pressure amplitudes that are many millions of times larger than the quietest sounds we can hear. Loud sounds can have intensities that trillions of times that of quiet sounds. The numbers are difficult to “grok” and even more inconvenient to work with. Sound levels use the math of logarithms to compress these wide-ranging numbers into something manageable. Examples of logs in science include the pH scale (for acids and bases in chemistry), the Richter scale (for earthquakes) and decibel (for sound).

There are two common (nearly identical) log scales for expressing sound amplitude: sound intensity level (SIL) and sound pressure level (SPL). SPL and SIL are essentially identical. Many people use SIL and SPL interchangeably, while others use the phrase sound level instead.

No matter which term you use, the word “level” is crucial- sound intensity level is not the same thing as sound intensity. Sound pressure is not the same thing as sound pressure level and so on.

Sound levels are expressed in decibels. Sound levels for common sounds cover a range of about 130 dB. (See chart below for sound levels for common sounds).

 Sound Sound Level (in dB) Sound Intensity (in pW/m2) Pressure Amplitude (in μPa) Hearing threshold 0 1 20 Quiet forest 10 10 60 Watch ticking 20 100 200 Rice crispies 30 1,000 600 Library 40 10,000 2,000 Floor fan 50 100,000 6,000 Conversation 60 1,000,000 20,000 Noise inside car 70 10,000,000 60,000 Vacuum cleaner 80 100,000,000 200,000 Leaf blower 90 1,000,000,000 600,000 Chain saw 100 10,000,000,000 2,000,000 Machine shop 110 100,000,000,000 6,000,000 Loud indoor arena 120 1,000,000,000,000 20,000,000 Jet takeoff 130 10,000,000,000,000 60,000,000

A quick look at the chart reveals that sound level is very a different thing than sound intensity. Every extra 10 dB corresponds to a sound that is ten times more intense than before.

### Stop to think 1

Does a 60 dB sound have twice the intensity of a 30 dB sound?

### Sound levels are relative

Sound levels show how a sound compares to a reference sound. The most commonly used reference sound is called the threshold of hearing– a barely audible pure tone at 1000 Hz that has a pressure amplitude of 20 μPa and an intensity of 1 pW/m2. The chart above uses the threshold of hearing as the reference sound.

Sometimes, other references are more convenient. For instance, recording engineers usually use the loudest sound that doesn’t cause distortion as the reference. Decibel values for sounds are often given without a mentioning a reference level (like in the table above). When this is done, it is usually safe to assume the reference is the threshold of hearing.

Elevation in geography works the same way. Elevations are relative to a reference level- almost always sea level. When Wikipedia gives the elevation on the floor of Death Valley as -86 meters, you assume the author means 86 meters below sea level. But, in some contexts, you could choose to use some other reference. For instance, if you’re climbing Mt. Everest, you might want to choose the top of Everest as the your reference level. Negative elevation means you’re not quite at the top yet.

### Stop to think 2

Can a sound have a negative sound level and still be heard?

### When is SIL different than SPL?

A sound’s SIL and SPL are always equal, unless different reference levels are used. If the SPL of a sound is expressed relative to human threshold of hearing, but the SIL is expressed  relative to the runway at JFK airport, the SPL and SIL won’t be equal.

### Just noticeable difference

Humans have trouble distinguishing between sounds with seemingly large differences in intensity- two jet planes don’t sound much louder than one. Most people have trouble telling which sound is louder when comparing sounds with levels that differ by less than 1 dB. For comparison, the “two jet” sound has a sound level that is only 3 dB more than the “one jet” sound. The smallest difference that can be perceived is called a just noticeable difference (JND). Humans are actually somewhat better at telling loud sounds apart than quiet ones- the JND drops from about 1.5 dB at 40 dB to about 0.5 dB at 90 dB.

### Hearing loss

Exposure to loud sounds can cause hearing loss. The damage can be profound and immediate or gradual. The amount of damage depends on the loudness of the sound and the duration of exposure. Sounds at levels below 75 dB are generally considered safe, even for prolonged exposure. However, sounds as low as 85 dB (heavy traffic in a city) can cause damage over with repeated and/or prolonged exposure. Power tools, lawn mowers, motorcycles, headphones at maximum volume have levels well above 85 dB. Some sounds (firecrackers, gunshots) are so loud that a single burst can cause immediate and profound hearing loss.

Noise induced hearing loss is generally avoidable by exercising common sense-

1. be aware of potentially dangerous sounds and avoid them,
2. limit your exposure to environments with sound levels over 75 dB and
3. wear appropriate hearing protection when doing loud activities.

Ear protection is not a cure-all, though. Even properly worn, professional quality ear plugs only reduce sound levels by 10 dB to 15 dB.

### Stop to think answers

1. No. Sound level is not the same thing as sound intensity. According to the chart, a 60 dB sound has an intensity that’s one thousand times that of the 30 dB sound (1,000,000 pW/m2 compared to 1,000 pW/m2).
2. Yes, if the reference level used for decibel scale is above threshold of hearing. (If the reference sound is a jet plane 30 meters away, almost all audible sounds will have a negative sound level).

## License

Understanding Sound Copyright © by dsa2gamba and abbottds is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.