The Physics of Musical Instruments
Acoustic resonance is the phenomenon where an acoustic system amplifies sound waves whose frequency matches one of its own natural frequencies of vibration (its resonance frequencies).
This is the exact principle behind every wind instrument, from a tiny flute to a massive church organ. By blowing air across an opening, you create a spectrum of white noise. The physical shape of the pipe "selects" and amplifies the specific frequencies that perfectly fit inside it as standing waves.
Open vs. Closed Pipes
The boundaries of the pipe determine how the standing waves form:
- Open Both Ends (Flutes, Open Organ Pipes): The wave has an "antinode" (maximum vibration) at both ends. The fundamental frequency (1st harmonic) fits half a wavelength inside the pipe.
- Closed One End (Clarinets, Stopped Organ Pipes): The wave has a "node" (zero vibration) at the closed end and an antinode at the open end. The fundamental frequency fits only a quarter of a wavelength inside the pipe, making the sound exactly one octave lower than an open pipe of the same length.
The Formula
Example Calculation
You have a pipe that is $1 , \text{meter}$ long, open at both ends. The speed of sound is $343 , \text{m/s}$. Find the fundamental frequency ($n=1$).
- Multiply n by Velocity: $1 \times 343 = 343$.
- Multiply Length by 2: $2 \times 1 = 2$.
- Divide: $343 / 2 = 171.5 , \text{Hz}$.
The pipe will resonate at $171.5 , \text{Hz}$ (roughly an F3 note).