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Next, two finite length string examples with different boundary conditions demonstrate how the boundary conditions restrict the frequencies that can form standing waves. Next, the example of sound waves in a pipe demonstrates how the same principles can be applied to longitudinal waves with analogous boundary conditions.
The resonance properties of a cylinder may be understood by considering the behavior of a sound wave in air. Sound travels as a longitudinal compression wave, causing air molecules to move back and forth along the direction of travel. Within a tube, a standing wave is formed, whose wavelength depends on the length of the tube.
The pipe is filled with the gas, and the gas leaking from the perforations is lit. If a suitable constant frequency is used, a standing wave can form within the tube. When the speaker is turned on, the standing wave will create points with oscillating (higher and lower) pressure and points with constant pressure (pressure nodes) along the tube.
An acoustic pipe, such as an organ pipe, marimba, or flute resonates at a specific pitch or frequency. Longer pipes resonate at lower frequencies, producing lower-pitched sounds. The details of acoustic resonance are taught in many elementary physics classes. In an ideal tube, the wavelength of the sound produced is directly proportional to the ...
They occur when waves are reflected at a boundary, such as sound waves reflected from a wall or electromagnetic waves reflected from the end of a transmission line, and particularly when waves are confined in a resonator at resonance, bouncing back and forth between two boundaries, such as in an organ pipe or guitar string. In a standing wave ...
The sound generator is turned on and the piston is adjusted until the sound from the tube suddenly gets much louder. This indicates that the tube is at resonance. This means the length of the round-trip path of the sound waves, from one end of the tube to the other and back again, is a multiple of the wavelength λ of the sound waves. Therefore ...
The Rijke tube is a cylindrical tube with both ends open, inside of which a heat source is placed that turns heat into sound, by creating a self-amplifying standing wave, due to thermo-acoustic instability. It is an entertaining phenomenon in acoustics and is an excellent example of resonance.
An acoustic waveguide is a physical structure for guiding sound waves. Sound in an acoustic waveguide behaves like electromagnetic waves on a transmission line. Waves on a string, like the ones in a tin can telephone, are a simple example of an acoustic waveguide. Another example are pressure waves in the pipes of an organ.