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The vibration of a perfect cylinder at its resonant frequency produces a standing wave pattern. The displacement waves in the pipe travel between positions of maximum and minimum pressure, as illustrated above. Each such displacement wave is called a compression wave, and the speaker is said to be in compression. A movement of the air within the pipe causes the pressure waves to travel from one end of the pipe to the other. When the pressure waves reach the end of the pipe, the pressure on the air is lower than it was at the other end of the pipe, and the pressure waves travel back through the air in the opposite direction, causing the speaker to be in rarefaction. In the cylinder, displacement waves travel with a velocity of, where T is the temperature in °C.
However, if the pipe is an imperfect cylinder, the pressure waves may travel through the air and the sound waves may be heard at the other end. For this reason, open pipes are often referred to as resonators.
The velocity of the displacement waves is equal to the velocity of sound in the air. If the speaker is placed at a distance of x from the end of the pipe, the displacement wave travels from one end of the pipe to the other in x/c seconds.
If the pipe were a perfect cylinder, the pressure waves would never reach the other end of the pipe and never travel through the air. To simulate a cylindrical pipe that is open at one end, the speaker can be modeled as a sphere. The surface of the sphere can be modeled as a perfect cylinder, which is open at both ends.
The amplitude of the pressure wave varies inversely with the distance from the speaker, as shown above. The amplitude of the displacement wave varies inversely with the distance from the speaker.
In the simple model of a cylindrical pipe, if the pipe is perfectly sealed at both ends, the pressure waves cannot leave the pipe. Only displacements can leave the pipe. This means that the amplitude of the displacement waves drops off exponentially with distance from the speaker.
Percussive waves are produced by a vibrating object. A vibrating object is one that vibrates in a direction parallel to its axis of symmetry, rather than transversely to it. For example, a hammer is a vibrating object. A vibrating object may or may not have a physical support. If there is a physical support, it need not be rigid. In the case of a vibrating object supported by a viscoelastic material, the support is elastic.
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