Sound

Waves
Waves in the context of this page are waves which propagate through a medium (solid, liquid, or gas) at a wave speed which depends on the elastic and inertial properties of that medium. There are two basic types of wave motion : longitudinal waves and transverse waves . In a longitudonal wave the medium motion is parallel to the direction of wave propagation In a transverse wave the medium movement is perpendicular to the direction of wave propagation.

Examples of periodic wave motions are

• A long rope, string or pipe shakes at one end results in traverse waves to move to the other end
• Waves in the sea is a combination of longtitudonal and transverse waves.
• Sound waves are essentially waves

Waves generally have a number of properties.

1. Period (T) is the time for a wave to complete one cycle
2. Frequency (f) is the number of cycles per unit time : f = 1 /T
3. Amplitude (A) The maximum value of the periodic wave on either side of the equilibrium position
4. Crest of a wave is the highest value of the wave above its equilibrium point.
5. Trough of a wave is the lowest value of the wave below its equilibrium point.
6. Wavelength g The distance between adjacent crests or troughs
7. Intensity (I) The rate of which the wave conveys energy

Sound
Sound waves are longitudonal waves which travel in solid liquids and gases. The transfer of energy is by the cyclic compression and expansion of the medium at the source. The velocity of sound in different mediums is listed below;

Velocities of sound (approximate) in various mediums at 0^o C

1. Velocity of Sound in dry air = 331.4 + 0,6.t m/s .....t= Temperature (Celsius)
2. Velocity of Sound in water = 1,540 m/s
3. Velocity of Sound in Pine Timber = 3,340 m/s
4. Velocity of Sound in Brick = 3660 m /s
5. Velocity of Sound in Steel = 5400 m /s

The loudness of sound is a perception of the comparative strength of the sensation received by the human ear. The useful measurement of sound is simple as sound is is largely a biological effect depending on the human ear. Sound mostly depends on the energy transferred to the human ear. The amount of energy in ergs which passes in one second through an area of 1 cm² is a measure of the intensity of sound

The loudness of sound varies as the square of the amplitude and inversely as the square of the distance from the source. This does not apply in an enclosed space or if the sound source is large compared to the distance of the listener . The ear perceives sound on a logarithmic level and is attuned to a small range of sound frequencies.

Sound level measurements in decibels are generally referenced to an accepted standard threshold of hearing at 1000 Hz for the human ear which can be stated in terms of sound intensity:

Threshold Level for human hearing I_o = 10 ^-16 Watts / cm² = 10 ^-9 ergs / s / cm²

The most accepted method of measuring relative sound level is by the use of the decibel scale.

I (dB) = 10 . log ₁₀. (I / I_o )

At the threshold level defined above the dB value is 0.
A sound energy level increase of 10 result is a db value of 10.
A sound energy level increas of 100 results in a dB value of 20

Common sound	Sound Level dB	Effect
Rocket launching pad (no ear protection)	180	Irreversible hearing loss
Carrier deck jet operation		Painfully loud
Air raid siren	130	Painfully loud
Thunderclap
Jet takeoff (200 ft)	120
Auto horn (3 ft)		Extremely Loud
Rock concert
Fireworks	100	Very Loud
Heavy Lorry (50 ft)	90
City traffic
Hearing damage (8 Hrs)
Alarm clock (2 ft)
Hair dryer	80	Annoying
Road traffic	70
Business office		Intrusive
Air conditioning unit	60
Conversational speech	50	Quiet
Light auto traffic (100 ft)
Quiet
Living room	50
Bedroom	40
Quiet office
Library	30	Very quiet
Soft whisper (15 ft)	20
Broadcasting studio
	10	Just Audible
	0	Hearing begins

Phons
The sound level measured in decibels does not take into accound the effect of sound frequency or pitch which in practice has a important effect on the perceived sound level. A method of measuring the relativ sound level at a fixed frequency (1000 HZ) result in a more representative value. The use of phons as a measurement unit relates to the relative sound level in dB at 1000HZ. e.g 70 phons = 70 dB at 1000 Hz.

Sones
The use of the phon as a unit of loudness is an improvement over just quoting the level in decibels, but it is still not a measurement which is directly proportional to loudness as heard by the human ear. Using the rule of thumb for loudness, the sone scale was created to provide such a linear scale of loudness.

The table below provides equivalent phon and sone values

Phons	20	30	40	50	60	70	80	90	100	120	130
Sones	0.25	0.5	1	2	4	8	16	32	64	128	256

Standard for Sound Level Measurement

ISO 226:2003. Acoustics -- Normal equal-loudness-level contours .....
This International Standard specifies combinations of sound pressure levels and frequencies of pure continuous tones which are perceived as equally loud by human listeners. The specifications are based on the following conditions: the sound field in the absence of the listener consists of a free progressive plane wave; the source of sound is directly in front of the listener; the sound signals are pure tones; the sound pressure level is measured at the position where the centre of the listener's head would be, but in the absence of the listener; listening is binaural; the listeners are otologically normal persons in the age range from 18 years to 25 years inclusive.