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Sound wave propagation

Sound wave propagation is a wave process. The acoustic signals requires a mechanical elastic medium for propagation and cannot travel through a vacuum unlike, electromagnetic light waves.
Sounds travels more quickly in solids, followed by liquid than through gases. The velocity of sound, in a wave form is 331.29 {ms}^-1 through dry air at {0}^oC

 Sound wave concept
When vibration disturbs particle in a medium, then the particle displaces other surrounding particles in that medium. A wave pattern is then formed, when the particle moves in the outward direction continuously. The wave carries the sound energy through the medium from the source and become less intense. The sound energy solely depends on the volume of the volume of the sound; the higher the sound energy the louder the volume.
There are three concept of sound wave that causes a sound to be produced. They include: frequency (f), wavelength \lambda and amplitude (A). The sound wave vibrates at different frequency as it moves through the medium. The sound wave may have single frequency or many frequencies depending on the source of the sound vibration.
Let us consider, a sound wave generated by a source at constant frequency with displacement function on the y-axis and time function of the x-axis as shown in fig. 1.
The number of sound wave generated per seconds is the frequency (f) of the sound and its unit is in Hertz (Hz). The maximum displacement of a peak is called amplitude (A) and the distance from one peak to another is called the wavelength \lambda.
The sinusoidal wave generates only single frequency while different non-repeated sounds generates different frequencies. Sound waves are longitudinal waves, this means that the wave medium for instance, air oscillates parallel to the wave's direction. 
Fig. 1

Air particle oscillates back and forth in a direction parallel to the sound waves movement, which creates compression and rarefaction wave alternately.
Longitudinal waves begins with compression then followed by rarefaction. The wavelength of the sound wave can be measured by comparing two consecutive compression or rarefaction.
Sound interference and Doppler effect
Sound interference is defined as when two sounds from different sources, cancels or superimpose each other's effect. The sound source that cancels or superimpose the effect produces no sound, whereas noise maybe produced from the sound source that was superimposed.
If the source of the sound is in motion, then the variable length might be generated; the wavelength of the sound wave  becomes short in one direction and extend in another direction. The pitch from the source of the sound is different by a stationary receiver who listens to it. This phenomenon is what is called the ''Doppler effect''. The Doppler effect was named after Christian Doppler who discovered it.
In Doppler effect, the frequency of the sound heard by the stationary receiver is different from the frequency of the actual sound source. The change in the frequency depends on the wavelength of the sound wave in motion from the stationary receiver. The frequency of the sound is increased as the sound source gets closer to the stationary receiver, thereby reducing the wavelength of the sound. Also, the frequency of the sound wave reduced as the sound source gets far away from the stationary receiver, because the wavelength is increased.
Sound absorption 
The sound wave interacts with the material or the object's surface and may be absorbed, transmitted, diffracted, refracted or reflected by the surface depending on the type of the material or object's surface. This phenomena is described diagrammatically in fig. 2. 
When all the emitted sound wave from the sound source are absorbed by the receiver, then it is said that sound absorption has occurred; just like a foam absorbing water. Sound absorption is an important process as far as sound insulation is concerned. Sound absorption may be of different types.
The sound absorbers maybe in porus or resonant types. The porus absorbent are classified into: fibrous material and open-celled foams. Fibrous materials converts acoustics energy into heat energy when sound impinges the absorber. For open-celled foam, sound waves displacement occurs through a tiny passage of foam, and may result to heat loss. Resonant absorbent are in mechanical form, where there is solid plates with tight air space behind it.
Note, that in some cases some materials such as the open-celled foam absorbs sound waves while glass materials blocks sound waves. The application of the sound wave depends on the end use. For example, a room may be built with sound absorbing or proofing materials.

Fig. 2

Sound absorption measures the amount of energy absorbed by the surface of a material or object; known as the sound absorption coefficient \alpha.
The sound absorption coefficient ranges from 0 to 1. Where 0 means there was no absorption by the surface and 1 means the highest or total absorption. The higher the sound absorption coefficient \alpha the lower the reverberation time.
The reverberation time is defined as the sound wave in space after the sound source has been stopped. It is also defined as the time duration of a sound to decay by 60dB after the sound source has been stopped. One major importance of sound absorption is that it makes acoustic environment suitable for specific purpose; such as: in recording studios, lecture halls etc.

Sound transmission
Sound transmission is a process the sound wave propagates through the medium to the receiver without any frequency loss.

Sound reflection
If a sound wave impinges on a hard  or smooth surface, the sound wave would reflect back without any frequency loss. The reflection angle of the sound wave from the surface or medium is equal to the angle of incidence. The angle of incidence is defined between the normal of the reflecting plane, the incidence and the reflecting waves. The angle of reflection, follow the Huygen's geomentry, where both the angle of reflection and angle of incidence are equal.
Echo is an example of sound reflection. The reason why sound echo is because, the sound wave perpendicular to the sound source hit a flat and smooth surface.

 Sound refraction
Sound wave refraction occurs when the sound wave is transmitted into the surface but the transmitted wave is bent away from the straight line of travel.
The factor that make sound to be refracted are: speed of sound, angles between sound propagation direction, wind direction, atmospheric conditions such as: relative humidity and temperatures etc.

Sound diffraction 
Sound diffraction involves a change in the direction of the sound wave as it propagates through the surface of a material or object. As the sound source move closer to the barrier, less sound diffraction is obtained.
Also, note that the sound at lower frequencies tends to diffract more easily than sounds at higher frequency.



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