Waveguide (acoustics)
Encyclopedia
An acoustic waveguide is a physical structure for guiding sound waves.
used aboard ships for communication between decks.
Other examples include the rear passage in a transmission line loudspeaker
enclosure, the ear canal
or a device like a stethoscope
. The term also applies to guided waves in solids.
A duct for sound propagation also behaves like a transmission line
(e.g. air conditioning duct, car muffler, etc.). The duct contains some medium
, such as air, that supports sound propagation. Its length is typically around quarter of the wavelength
which is intended to be guided, but the dimensions of its cross section
are smaller than this. Sound is introduced at one end of the tube by forcing the pressure
to vary in the direction of propagation, which causes a pressure gradient to travel perpendicular to the cross section at the speed of sound
. When the wave reaches the end of the transmission line, its behaviour depends on what is present at the end of the line. There are three generalized scenarios:
A low impedance
load (e.g. leaving the end open in free air) will cause a reflected wave in which the sign of the pressure variation reverses, but the direction of the pressure wave remains the same.
A load that matches the characteristic impedance (defined below) will completely absorb the wave and the energy
associated with it. No reflection
will occur.
A high impedance load (e.g. by plugging the end of the line) will cause a reflected wave in which the direction of the pressure wave is reversed but the sign of the pressure remains the same.
Since a transmission line behaves like a four terminal model, one cannot really define or measure the impedance of a transmission line component. One can however measure its input or output impedance. It depends on the cross-sectional area and length of the line, the sound frequency, as well as the characteristic impedance of the sound propagating medium within the duct. Only in the exceptional case of a closed end tube (to be compared with electrical short circuit), the input impedance could be regarded as a component impedance.
Where a transmission line of finite length is mismatched at both ends, there is the potential for a wave to bounce back and forth many times until it is absorbed. This phenomenon is a kind of resonance
and will tend to attenuate any signal fed into the line.
When this resonance effect is combined with some sort of active feedback mechanism and power input, it is possible to set up an oscillation
which can be used to generate periodic acoustic signals such as musical notes (e.g. in an organ pipe).
The application of transmission line theory is however seldom used in acoustics
. An equivalent four terminal model which splits the downstream and upstream waves is used. This eases the introduction of physically measurable acoustic characteristics, reflection coefficient
s, material constants of insulation
material, the influence of air velocity on wavelength (Mach number), etc. This approach also circumvents impractical theoretical concepts, such as acoustic impedance of a tube, which is not measurable because of its inherent interaction with the sound source and the load of the acoustic component.
Examples
One example might be a speaking tubeSpeaking tube
A speaking tube or voicepipe is a device based on two cones connected by an air pipe through which speech can be transmitted over an extended distance. While its most common use was in intra-ship communications, the principle was also used in fine homes and offices of the 19th century, as well as...
used aboard ships for communication between decks.
Other examples include the rear passage in a transmission line loudspeaker
Loudspeaker
A loudspeaker is an electroacoustic transducer that produces sound in response to an electrical audio signal input. Non-electrical loudspeakers were developed as accessories to telephone systems, but electronic amplification by vacuum tube made loudspeakers more generally useful...
enclosure, the ear canal
Ear canal
The ear canal , is a tube running from the outer ear to the middle ear. The human ear canal extends from the pinna to the eardrum and is about 35 mm in length and 5 to 10 mm in diameter....
or a device like a stethoscope
Stethoscope
The stethoscope is an acoustic medical device for auscultation, or listening to the internal sounds of an animal body. It is often used to listen to lung and heart sounds. It is also used to listen to intestines and blood flow in arteries and veins...
. The term also applies to guided waves in solids.
A duct for sound propagation also behaves like a transmission line
Transmission line
In communications and electronic engineering, a transmission line is a specialized cable designed to carry alternating current of radio frequency, that is, currents with a frequency high enough that its wave nature must be taken into account...
(e.g. air conditioning duct, car muffler, etc.). The duct contains some medium
Transmission medium
A transmission medium is a material substance that can propagate energy waves...
, such as air, that supports sound propagation. Its length is typically around quarter of the wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
which is intended to be guided, but the dimensions of its cross section
Cross section (geometry)
In geometry, a cross-section is the intersection of a figure in 2-dimensional space with a line, or of a body in 3-dimensional space with a plane, etc...
are smaller than this. Sound is introduced at one end of the tube by forcing the pressure
Pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...
to vary in the direction of propagation, which causes a pressure gradient to travel perpendicular to the cross section at the speed of sound
Speed of sound
The speed of sound is the distance travelled during a unit of time by a sound wave propagating through an elastic medium. In dry air at , the speed of sound is . This is , or about one kilometer in three seconds or approximately one mile in five seconds....
. When the wave reaches the end of the transmission line, its behaviour depends on what is present at the end of the line. There are three generalized scenarios:
A low impedance
Acoustic impedance
The acoustic impedance at a particular frequency indicates how much sound pressure is generated by a given air vibration at that frequency. The acoustic impedance Z is frequency dependent and is very useful, for example, for describing the behaviour of musical wind instruments...
load (e.g. leaving the end open in free air) will cause a reflected wave in which the sign of the pressure variation reverses, but the direction of the pressure wave remains the same.
A load that matches the characteristic impedance (defined below) will completely absorb the wave and the energy
Energy
In physics, energy is an indirectly observed quantity. It is often understood as the ability a physical system has to do work on other physical systems...
associated with it. No reflection
Reflection (physics)
Reflection is the change in direction of a wavefront at an interface between two differentmedia so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves...
will occur.
A high impedance load (e.g. by plugging the end of the line) will cause a reflected wave in which the direction of the pressure wave is reversed but the sign of the pressure remains the same.
Since a transmission line behaves like a four terminal model, one cannot really define or measure the impedance of a transmission line component. One can however measure its input or output impedance. It depends on the cross-sectional area and length of the line, the sound frequency, as well as the characteristic impedance of the sound propagating medium within the duct. Only in the exceptional case of a closed end tube (to be compared with electrical short circuit), the input impedance could be regarded as a component impedance.
Where a transmission line of finite length is mismatched at both ends, there is the potential for a wave to bounce back and forth many times until it is absorbed. This phenomenon is a kind of resonance
Resonance
In physics, resonance is the tendency of a system to oscillate at a greater amplitude at some frequencies than at others. These are known as the system's resonant frequencies...
and will tend to attenuate any signal fed into the line.
When this resonance effect is combined with some sort of active feedback mechanism and power input, it is possible to set up an oscillation
Oscillation
Oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. Familiar examples include a swinging pendulum and AC power. The term vibration is sometimes used more narrowly to mean a mechanical oscillation but sometimes...
which can be used to generate periodic acoustic signals such as musical notes (e.g. in an organ pipe).
The application of transmission line theory is however seldom used in acoustics
Acoustics
Acoustics is the interdisciplinary science that deals with the study of all mechanical waves in gases, liquids, and solids including vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of acoustics...
. An equivalent four terminal model which splits the downstream and upstream waves is used. This eases the introduction of physically measurable acoustic characteristics, reflection coefficient
Reflection coefficient
The reflection coefficient is used in physics and electrical engineering when wave propagation in a medium containing discontinuities is considered. A reflection coefficient describes either the amplitude or the intensity of a reflected wave relative to an incident wave...
s, material constants of insulation
Soundproofing
Soundproofing is any means of reducing the sound pressure with respect to a specified sound source and receptor. There are several basic approaches to reducing sound: increasing the distance between source and receiver, using noise barriers to reflect or absorb the energy of the sound waves, using...
material, the influence of air velocity on wavelength (Mach number), etc. This approach also circumvents impractical theoretical concepts, such as acoustic impedance of a tube, which is not measurable because of its inherent interaction with the sound source and the load of the acoustic component.