How sound is generated

Sound comes from a series of pressure pulses that reach our ears through the air around us. A vibrating surface is one way to generate these pressure pulses: the surface compresses the air as it moves forwards and reduces the pressure (rarifies) the air as it moves backwards. These compressions and rarefactions produce a type of oscillating wave known as a longitudinal wave, because the variation in pressure is in the same direction as the wave travel. You can visualise this using a Slinky spring. If you hold the spring at both ends and move one end to and fro along the spring's length, you can see these pressure pulses travel towards the other end of the spring.

Another way that pressure fluctuations can be made is through turbulence in the air. Turbulence can be caused when fast-moving air moves round an object and meets slower-moving air behind it, causing it to change direction and initiating a swirling motion in the air. Changes in air velocity also occur when it passes over a surface and slows down through friction. The viscosity of the air transfers these retarding forces further out into the free stream, causing a velocity gradient near the surface, once again causing turbulence under certain conditions.

These pressure fluctuations are very small compared with most static pressures we are familiar with. The pressure of the atmosphere around us is around 100 000 pascals. The pressure in a bicycle tyre is four times greater still. What we are talking about with sound waves is the variation of pressure around this static level, which amounts to no more than a few pascals even for the loudest sounds. Here, we can detect a pressure variation of 20 pascals in 100 000. In fact, it is remarkable just how sensitive our ears can be. To detect the quietest sounds, we need to detect a variation of 0.00002 pascals in 100 000, a variation of one part in five thousand million.

How sound is detected - or how to talk loudly over a million mice

A sound wave is detected in our ears by microscopic hairs called cilia that are sensitive enough to be moved by these tiny pressure fluctuations. http://www.harvardmagazine.com/on-line/030575.html

Our ears are capable of registering sounds from the tiny scratching sounds of a mouse all the way up to the roar of a jet engine on take-off, which is roughly a million, million times louder. This enormous range of sound levels means our ears have the widest dynamic range of any of our senses. So how can the sound of a mouse and the sound of a jet engine be represented on the same scale? If a mouse's sound moved a sound meter needle just 1 mm along the scale, the jet engine would move the needle one million kilometres - that's almost three times further away than the moon.

The decibel (dB) scale

A linear scale is clearly an impractical way of measuring sound. Instead, a logarithmic scale must be used. If you remember your laws of indices, we can represent any number as a "power of ten". Ten is ten to the power one, a hundred is ten squared or ten to the power two, a thousand is ten to the power three and so on. The number two, for instance, is approximately 10 to the power 0.301. There is a special name for this "power of ten" - it is called the logarithm of the number. So if we think in terms of logarithms, we can start to measure huge numbers really easily: each time the number gets ten times bigger, the logarithm goes up by one. This scale was first used by electrical engineers who, like acousticians, also have to deal with very wide-ranging signals. The scale they developed was named after a famous electrical engineer and inventor called Alexander Graham Bell. One Bel (with one "L", note!) represents a factor of ten. As this is rather a big ratio for many measurements, they started to measure things in tenths of a Bel, or deci-Bel and so the modern decibel scale was born (symbol dB).

You may have noticed by now that I keep talking about "a factor of ten" and "ratios". That is because I have been talking about how much louder a jet engine is than a mouse; in other words, I have to compare two sounds if I want to use a dB scale. The sound used for comparison is known as the reference level. The dBs tell me how much louder the measured sound is compared with this reference level. So a ratio of a million million to one means the jet engine is ten to the power 12 times louder than the mouse, or 12 Bels. The deci-Bel is 10 times smaller, so this would measure 12 x 10 = 120 dB on my sound level meter. A conversation in a noisy office would measure about 60 dB. If you could cram a million mice into the office, they would make about the same amount of noise (no squeaking, of course, only scratching!). Surprising, isn't it?

The electrical engineers were interested in measuring the power in their circuits, so the decibel scale is defined in terms of power. Acousticians are interested in sound power, so the scale works well for us too. The definition is as follows:
Value on the Bel scale = log(power level of interest/ reference power) And
Value on the decibel scale = 10 x log(power level of interest/reference power)

Electrical engineers might use 1 watt as their reference level. Acousticians have to use an even smaller quantity: a million million times smaller in fact: 1 pico-watt. Unfortunately, we cannot measure sound power directly - we can only detect sound pressure fluctuations using microphones instead of our ears. It was discovered that sound power is related to sound pressure squared. So we have to take the sound pressure ratio and square it first before finding its logarithm. An acoustic level can be measured on the decibel scale as:
Acoustic dB = 10 x log[(sound pressure / reference pressure) squared]

The standard reference sound pressure level in air is 20 micro-pascals. How small is that? A pascal is a unit of pressure equal to a force of one newton applied over an area of one square metre. To give you an idea, a newton is about the weight of an eating apple. Easy to remember when you think of Isaac Newton supposedly coming up with his ideas on gravity after being struck on the head by an apple! So there is our apple resting on a one metre square tray. Now imagine that apple cut into a million pieces and leaving only 20 of them on the tray. Our ears could detect whether that tiny pressure was there or not. For comparison, if you jump up and down on a paving slab you exert a pressure fluctuation on the ground of around 1000 pascals, so our ears can detect something 50 million times smaller.

Here is another link with some example sound files. At one point here, they refer to the decibel scale as having "units" of dB. This is not strictly true: because it is derived from a ratio of two quantities with the same units, the end result is dimensionless - it has no units. It is simply a convenient way of saying that something is many times greater or smaller than the chosen reference level. But I'm being picky; it is a good site with some interesting material.< a href="http://www.phys.unsw.edu.au/~jw/dB.html">http://www.phys.unsw.edu.au/~jw/dB.html