Stationary Waves In Air Columns
This lesson covers:
- How longitudinal stationary sound waves are produced in wind instruments and other air columns
- Conditions for resonance and stationary wave formation in open and closed pipes
- The relationships between pipe length, wavelength, and the lowest resonant frequency
Longitudinal stationary waves in wind instruments
In wind instruments, a vibrating source at one end sets up longitudinal stationary sound waves within the air column. Areas of compression and rarefaction form at fixed positions.
For an open pipe:
- Antinodes occur at the open ends.
- The lowest frequency is produced when length l = λ/2.
For a closed pipe:
- A node occurs at the closed end.
- The lowest frequency has l = λ/4.
Conditions for resonance and stationary waves
Resonance occurs when:
- The frequency matches a natural frequency of the air column.
- Constructive interference produces stationary waves.
The pipe length dictates which wavelengths, and hence frequencies, can resonate.
Relating length and wavelength to resonant frequency
For an open pipe with length l:
- Minimum l = λ/2 for the 1st harmonic
- Higher harmonics have l = λ, 3λ/2 etc.
For a closed pipe with length l:
- Minimum l = λ/4 for the 1st harmonic
- Higher harmonics have l = 3λ/4, 5λ/4 etc.
Since v = fλ, shorter lengths produce higher resonant frequencies.