Thursday, October 26, 2006

All About Sound, Part 7

Another installment!! This is the latest installment of Scott Janus' "Audio in the 21st Century" from Audio DesignLine. Part 7 talks about measuring sound intensity and power.

In this article, he covers the basic math computations using the logarithmic scale and decibels. He briefly mentions that human hearing is not linear -- we can hear slight changes at low levels, but don't notice similar differences at high volumes. I think he plans to discuss this topic in more detail in a later installment.

In case he doesn't mention this... I thought I would go ahead and offer a little more detail. As mentioned in earlier installments, sound is created when something strikes another object. So when a guitar string vibrates, it is striking against air molecules. The vibrations cause the air nearby to compress and expand. A shorter string vibrates at a faster rate than a longer string, creating a higher pitched sound... The more compressed (or expanded), the more energy it contains and can expend. The loudness, or intensity of the sound is measured in terms of the amount of energy passing each second through one square centimeter of area. Energy expended over time is power and the unit is the watt. A watt is one joule per second. As you know, a 75 watt light bulb is pretty bright. A 40 watt bulb, not so bright. One of those small little night lights used to find the bathroom without bumping into a wall is probably around 1/4 watt. The amount of power found in sound is really small. The amount of power carried by ordinary conversational sound is about 1/1000 watt.

The human ear detects the difference in loudness by ratios of the power, not the actual differences. So, a 2000 microwatt (1/2000 watt) sound will seem louder than a 1000 microwatt sound, but a 3000 microwatt sound will not seem to sound louder by as much again. It actually takes a 4000 microwatt sound to seem louder by as much as a 2000 microwatt sound compares to a 1000 microwatt sound. To get a sound that is as much louder again than a 4000 microwatt sound, we would need an 8000 microwatt sound. The rations 2000/1000, 4000/2000, and 8000/4000 are all equal even though the difference are not, and it is the ratios that the ear detects.

This is where he explains that we don't hear linearly, but on a logarithmic scale. When one sound carries 10 times the power of a second sound, the ratio of the first to the second is 10 and the log (base 10) of this is 1. The difference in sound power is then said to be one 'Bel'. If a sound is 100 times more powerful than another sound, it is two Bels louder, 1000 times would be 3 Bels, etc. Since the Bel is too large of a scale for practical use, we use the decibel, which is 1/10th a Bel. A sound is a decibel louder than another when the first is 1.26 times as powerful as the second -- log(1.26) is about equal to 0.10.

The decibel is used one of two ways:
  1. to measure power or intensity
  2. to measure amplitude
The equation used to to measure sound power is (10 * log(N1/N2)). To measure sound amplitude we use the equation (20 * log(N1/N2)). So, a sound that is 10 times louder than a second sound (20 * log(10/1)) = 20 decibels. A sound that is twice as loud (20 * log(2/1)) = 6.02 decibels.

When dealing with these ratios, they use a standard reference for the denominator. For sound power or intensity, the denominator is the threshold of hearing (about the sound of a mosquito flying about 3 meters away), which is about 10-12 watts/m2. Sound pressure level (SPL) is usually used to specify the sound intensity. The upper limit of sound, before it behaves like a shock wave is about 194 dB (SPL). For comparison, windows break at about 163 dB; the sound of a jet engine from 30 meters (100 feet) is about 150 dB; the threshold of pain is about 130 dB; the sound of a train horn from 1 meter is about 120 dB and at this level can cause immediate perforation of your ear drum (so don't stand too close to a train when the horn goes off); and, loud music in a dance club is probably at 100 dB. They say anything above 85 dB is considered harmful and over 95 dB for long periods is considered unsafe.

BTW, so far, no one has entered the contest. I wonder why...? Is it the award -- no one likes beer or cheese? If so, any recommendations for a more enticing award? Is it because no one likes taking tests? Oh come on, it should be easy. All you have to do is read the articles. Is it because no one is reading those articles? (I know, I know, not many people are even reading this blog, so I'd really like to come up with useful info that potential readers find interesting). I'd really like some feedback on this. If there is a response, I might go ahead and post another test covering the later installments and award the winner with something like a gift certificate from Amazon.

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