Reflexion einer Druckwelle am geschlossenen Ende eines Rohres

A pressure oscillation resonance in a pipe closed on both sides, referred to as a closed tube resonance or closed-end resonance, occurs when sound waves within the pipe generate a standing wave pattern due to wave reflections at the closed ends. Here are the key points to understand about it:

  • Standing waves: When a sound wave propagates through a pipe closed on both ends, it undergoes reflection at each end. The resulting interference between the incoming and reflected waves gives rise to a stationary pattern known as a standing wave. Within the pipe, specific locations exhibit points of minimal displacement (nodes) and points of maximal displacement (antinodes).

  • Resonance frequencies: Closed pipe resonance transpires at distinct frequencies associated with the fundamental frequency and its harmonics. The fundamental frequency represents the lowest resonant frequency at which the fluid within the pipe can vibrate. The higher harmonics are integer multiples of the fundamental frequency.

  • Pipe length and resonance: The length of the pipe determines the wavelengths that can fit within it, thereby establishing the frequencies at which resonance occurs. The fundamental frequency in a pipe with both ends closed is inversely proportional to the pipe length. Mathematically, the fundamental frequency (f) is expressed as f = a / (2L), where a represents the speed of sound in the medium and L denotes the length of the pipe.

  • Node and antinode positions: In closed pipe resonance, the closed ends of the pipe function as nodes for the flow, indicating no displacement at these points but as antinodes for the pressure. The positions of nodes and antinodes within the standing wave pattern depend on the resonance mode (fundamental or harmonic) and the pipe length.

  • Sound production: Pressure oscillations occurring within the pipe, resulting from the standing waves, lead to the generation of sound. The pipe acts as a resonator, amplifying specific frequencies dictated by its length.

It is essential to note that the information provided here assumes idealized conditions and simplifications. Real-world scenarios may involve additional factors, such as pipe geometry, wall properties, and damping effects, which can influence the precise behavior of pressure oscillation resonances in closed pipes.

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