If the length of a pipe is increased, does the fundamental...

Name: Problem 25, Chapter 14: Pearson Physics
Uploaded: 2023-03-04T17:53:26-08:00
Duration: 2 min 10 s
Channel: Prabhu Ramji
Description: If the length of a pipe is increased, does the fundamental frequency increase, decrease, or stay the same? Does your answer depend on whether the pipe is open at both ends or closed at one end? Explain.

If the length of a pipe is increased, does the fundamental frequency increase, decrease, or stay the same? Does your answer depend on whether the pipe is open at both ends or closed at one end? Explain.

Key Concepts

Resonant Modes

Resonant modes refer to the specific patterns of standing waves that form in a system. The fundamental mode is the primary mode of vibration with the simplest standing wave pattern. In pipes, the resonant mode not only determines the fundamental frequency but also varies based on whether the pipe is open at both ends or closed at one end, thereby influencing the harmonic series of the instrument.

Boundary Conditions in Acoustics

The boundary conditions of a pipe—whether the ends are open or one end is closed—affect the standing wave patterns inside the pipe. In an open pipe, both ends support antinodes, while in a pipe closed at one end, there is a displacement node at the closed end and an antinode at the open end. These conditions alter the mathematical relation between the length of the pipe and the wavelength of the fundamental frequency, but the inverse relationship with length remains.

Relationship between Pipe Length and Frequency

For both open and closed pipes, the frequency decreases as the length of the pipe increases. This is because a longer pipe supports a longer wavelength for the fundamental mode, leading to a lower frequency according to the equation f = v/?.

Fundamental Frequency

The fundamental frequency is the lowest frequency at which a system naturally vibrates. In the context of pipes, it is determined by the speed of sound in the medium and the effective wavelength of the standing wave produced in the pipe. The basic relation shows that the frequency is inversely proportional to the length of the pipe.

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