Noise is any unwanted sound.  Somebody's music is, to another person, noise.  Noise can be distressing and there are procedures to stop any nuisance.

As far as physics is concerned, noise is any sound that propagates as a longitudinal wave in air, or a solid, or a liquid.  Energy is transmitted.  The intensity or energy flux is the energy per unit area, and is measured in watts per square metre (W m^-2)  The amplitude is measured as a pressure which has units of Pascal (Pa), and the human ear can detect pressure differences of 2 × 10^-5 Pa.  Atmospheric pressure is 10⁵ Pa.  A pressure difference of 2 × 10^-5 Pa corresponds to a movement of about the width of a hydrogen atom.

Like all progressive waves, the intensity of sound waves decreases by an inverse square law.

I µ r²

Double the distance, and the sound intensity goes down by 4 times.

The intensity of the quietest sound we can hear is about 1 × 10^-12 W m^-2, while normal conversation is about 1 × 10^-6 W.

Sound engineers measure sound levels on the decibel scale, using the sound intensity level of 1 × 10^-12 W m^-2 as a zero reference point.  There is another factor that has to be taken into account, which is the sensitivity of the ear to different frequencies; the human ear is not very sensitive to frequencies of 100 Hz (the frequency of speech) but very sensitive to 3000 Hz (the pitch of a human scream).

The scale works on the ratio of a sound intensity compared with the reference.  Consider this example comparing normal conversation with the sound of silence. 

Ratio = intensity of normal conversation =  1 × 10^-6 W m^-2 = 1 × 10⁶

           intensity of quietist audible sound   1 × 10^-12 W m^-2 

 So the sound of a normal conversation is 10⁶ times louder than the quietest audible sound.   We can do similar calculations with other sounds.  What we find is that the decibel scale is logarithmic.  1 bel is one power of ten,  So if we have six powers of ten, we have 6 bels.

To make the scale more usable, we talk about decibels, where 1 bel = 10 decibels (1dB = 10 B).  If a sound level goes up from 40 dB to 80 dB, the intensity has NOT doubled, but gone up 4 powers of 10, i.e. 10 000 times.

Noise Pollution

Noisy environments are unpleasant to live in.  They can lead to a range of psychological problems such as tension and anger in some people, to anxiety and depression in others.

In a work place, ear defenders must be worn if the sound level is greater than 85 dB.  Ear plugs reduce the intensity from 85 to 75 dB, reducing the level to 10 % of what it was.

Temporary exposure to loud noises can lead to dullness in hearing as the sensory cells get tired.  You can get a ringing sound, called tinnitus.   Prolonged exposure leads to permanent hearing damage.  If a personal stereo can be heard by other people in a train, then the chances are that it is far too loud.

Sound Control

Sound insulating materials work by absorbing the sound waves.  The materials:

• have a large surface area;

• deform plastically (the collisions with air molecules are inelastic).

So the air molecules lose kinetic energy, making the insulation heat up a tiny amount.

The noise in blocks of flats can be transmitted through walls and floors.  A good way of stopping the noise is to have sound insulation between a two lead wall as shown in the diagram:

The insulation absorbs much of the sound.  What sound that does get through is reflected by the second wall.  This is much more effective than a single thick wall.

Aeroplanes are noisy things.  They have to be kept as light as possible, so the engines can't have a silencer like a car.  Nor can they have much insulation.  The traditional way of reducing the impact of the noise on the pilots has been for them to wear sound absorbing headphones, in which there are speakers for the pilots to hear the air traffic controllers.

Modern aircraft head sets have an electronic system that picks up the outside noise, and inverts it through 180^o so that the waves superpose and cancel each other out.  It's not quite 100 % effective, but it makes a real difference.  These are called active noise control (ANC) headphones.

They are not cheap.

Other active noise control devices include "magic wallpaper" and smart materials.  The principle is the same; getting the material to make a wave in antiphase to the source wave.

Acoustics

Acoustics is a major application of the physics of sound.  There are many rooms where at one point you can hardly hear a speaker, but others you can hear the speaker quite clearly.  This is to do with the reflection patterns about a room.  A room full of people sounds a lot different to the same room when empty.  This is because peoples' bodies are good sound absorbers.

Large halls can be a problem.  As sound travels at 300 m/s, the time to travel 60 metres is 0.2 s.  This, combined with the echoes of solid walls can make the acoustics very poor.  Music becomes a jumble of noises, making it unpleasant, or even impossible to listen to.  Many old buildings have this problem, because the architects had little idea of acoustics.  Even a small change to an acoustically good hall can change the acoustics for the worse.

Various devices can be fitted to improve the acoustic performance of a hall.  The Royal Albert Hall in London has discs suspended from the ceiling, which has improved it no end.

Loudspeakers for Hi-Fi systems are tested in anechoic chambers, where sound is not reflected at all.  However it is not a good listening environment; the sound is very "dead"