THEORY

Sound waves travel outward in straight lines from their source until something interferes

with their path. During the refraction of sound waves, the waves enter a different material at

an angle other than 90 degrees, it is bent from its original direction, and there will be a

change in the angle of the direction. Because of the angle, part of the wave enters the new

medium first and changes speed. The difference in speeds causes the wave to bend. The

velocity of sound in each material properties, for example density for that material.

The sinusoidal wave is the most commonly used graphic representation of sound waves.

The properties of sine wave consists of frequency, which is the number of cycles per second,

amplitude (variations in air pressure) measured in decibels, wavelength, which is the length

of 1 period, of a wave, measured in metre per second, and lastly the phase, which is the

starting point of a wave along the y-axis, measured in degrees.

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Mathematically, the one-dimensional sine wave (or harmonic wave or sinusoid) with an

amplitude described by the equation:

where,  is the maximum amplitude of the wave, maximum distance from the highest point

of the disturbance in the medium (the crest) to the equilibrium point during one wave cycle.

In the illustration to the right, this is the maximum vertical distance between the baseline and

the wave,  is the space coordinate,  is the time coordinate,  is the wavenumber,  is

the angular frequency and  is the phase constant.

The units of the amplitude depend on the type of wave. Transverse mechanical waves

(e.g., a wave on a string) have an amplitude expressed as a distance (e.g., meters),

longitudinal mechanical waves (e.g., sound waves) use units of pressure (e.g., pascals), and

electromagnetic waves (a form of transverse vacuum wave) express the amplitude in terms of

its electric field (e.g., volts/meter).

The wavelength   is the distance between two sequential crests or troughs (or other

equivalent points), generally is measured in meters. A wavenumber  , the spatial frequency

of the wave in radians per unit distance (typically per meter), can be associated with the

wavelength by the relation

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The period   is the time for one complete cycle of an oscillation of a wave.

The frequency   is the number of periods per unit time (per second) and is typically

measured in hertz. These are related by:

In other words, the frequency and period of a wave are reciprocals. The angular frequency   

represents the frequency in radians per second. It is related to the frequency or period by

The wavelength   of a sinusoidal waveform traveling at constant speed   is given by:

where,   is called the phase speed (magnitude of the phase velocity) of the wave and   is the

wave's frequency.

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