A pipe is a cylindrical tube that is used to produce sound through resonance. It can be made of various materials such as metal, wood, or plastic and can vary in length and diameter.
A resonant mode is a specific frequency at which a pipe can vibrate and produce a standing wave. In a pipe with a closed end, the resonant mode occurs when the length of the pipe is equal to a quarter of the wavelength of the sound wave. In a pipe with open ends, the resonant mode occurs when the length of the pipe is equal to a half of the wavelength.
A node is a point in a standing wave where there is no displacement of the medium. In a pipe, a node occurs at the exact center of the pipe, where the pressure is always at ambient level.
The node in the exact center of a pipe is important because it allows for the formation of a standing wave in the pipe. This standing wave is responsible for the resonance and production of sound in the pipe.
The position of the node affects the resonant frequencies of a pipe because it determines the length of the pipe that is in resonance. For a pipe with closed ends, the length of the pipe must be equal to a quarter of the wavelength, and for a pipe with open ends, the length must be equal to a half of the wavelength. Therefore, the position of the node directly affects the resonant frequencies that can occur in a pipe.