Interactive physics simulator
Open Pipe
Explore how an air column open at both ends forms standing sound waves. Watch displacement antinodes, pressure nodes, harmonics, tuning, and pipe length change the pitch.
Open Pipe Resonance Simulator
Adjust pipe length, sound speed, radius, and harmonic number. The simulator shows displacement standing waves, pressure standing waves, air particle motion, and live resonance frequency.
Live Wave Telemetry
- Harmonic
- n = 1
- Frequency
- 264 Hz
- Length
- 0.65 m
- Wavelength
- 1.30 m
- Nodes / Antinodes
- P nodes 2
- End Correction
- 0.024 m
What is an Open Pipe?
An open pipe is a tube of air open at both ends, such as an ideal flute, organ pipe, or classroom resonance tube with two open mouths. At each open end, air can move freely, so the displacement of air particles is maximum. These open ends are displacement antinodes and pressure nodes.
Open pipes form longitudinal standing waves when sound reflections inside the tube reinforce each other. Because both ends have the same boundary condition, all integer harmonics are allowed.
Key Definition
- Both ends are open to air.
- Open ends are displacement antinodes.
- Open ends are pressure nodes.
- All integer harmonics are possible.
- Shorter pipe length gives higher pitch.
Open Pipe Formula
λn = 2Leff / n
fn = n v / 2Leff
With end correction: Leff = L + 2e and e ≈ 0.6r.
Open vs Closed Pipe
| Feature | Open pipe | Closed pipe |
|---|---|---|
| Ends | Both open | One closed |
| Displacement | Antinode at both ends | Node at closed end |
| Harmonics | All harmonics | Odd harmonics only |
| Fundamental | f = v / 2L | f = v / 4L |
Real-life Example
A flute behaves approximately like an open pipe. Opening a tone hole makes the effective air column shorter, so the wavelength becomes shorter and the pitch becomes higher.
- Longer air column: lower note.
- Shorter air column: higher note.
- Warmer air: slightly higher pitch.
Solved Examples
An open pipe has length 0.85 m. If sound speed is 340 m/s and end correction is ignored, find the fundamental frequency.
- For an open pipe, the fundamental wavelength is λ1 = 2L.
- λ1 = 2 × 0.85 = 1.70 m.
- Frequency is f = v / λ.
- f1 = 340 / 1.70 = 200 Hz.
Answer: Fundamental frequency = 200 Hz
A flute behaves approximately like an open pipe. What length gives A4, 440 Hz, if sound speed is 343 m/s and end correction is ignored?
- Use f1 = v / 2L for the fundamental mode.
- Rearrange to L = v / 2f.
- L = 343 / (2 × 440) = 0.390 m.
- A real flute uses tone holes and end correction, so its physical tube length is adjusted from this ideal value.
Answer: Ideal open-pipe length = 0.390 m
For an open pipe of effective length 0.50 m, find the first three harmonic frequencies if v = 340 m/s.
- For an open pipe, fn = n v / 2Leff.
- Fundamental: f1 = 1 × 340 / (2 × 0.50) = 340 Hz.
- Second harmonic: f2 = 2 × 340 = 680 Hz.
- Third harmonic: f3 = 3 × 340 = 1020 Hz.
Answer: f1 = 340 Hz, f2 = 680 Hz, f3 = 1020 Hz
Common Mistakes
- Forgetting that open ends are displacement antinodes.
- Using the closed-pipe formula for an open pipe.
- Forgetting both open ends need end correction.
- Thinking open pipes have only odd harmonics.
- Mixing pressure nodes with displacement nodes.
Practice Questions
1. What boundary condition forms at each open end of an open pipe?
Each open end forms a displacement antinode and a pressure node because air is free to move but pressure variation stays near atmospheric pressure.
2. An open pipe is 1.2 m long. If v = 336 m/s, find the fundamental frequency ignoring end correction.
Use f1 = v / 2L = 336 / (2 × 1.2) = 140 Hz.
3. Why does an open pipe support both odd and even harmonics?
Both ends have the same boundary condition, so any integer number of half-wavelengths can fit in the pipe: L = nλ/2.
4. If pipe length increases, what happens to resonant frequency?
The resonant frequency decreases because f is inversely proportional to effective pipe length.
Quick Summary
- Open pipes have both ends open.
- Both open ends are displacement antinodes and pressure nodes.
- The ideal formula is fn = n v / 2L.
- With end correction, use L + 2e instead of L.
- Open pipes support all harmonics.
Frequently Asked Questions
What is an open pipe in physics?
An open pipe is an air column open at both ends. It can support standing sound waves whose ends behave as displacement antinodes and pressure nodes.
What is the formula for an open pipe?
For an ideal open pipe, fn = n v / 2L. With end correction, use fn = n v / 2(L + 2e).
What is the fundamental frequency of an open pipe?
The fundamental frequency is the lowest resonant frequency. For an ideal open pipe, f1 = v / 2L.
What are nodes and antinodes in an open pipe?
Displacement antinodes occur at both open ends. For pressure, the open ends are pressure nodes.
Does an open pipe have all harmonics?
Yes. An open pipe supports all integer harmonics: first, second, third, fourth, and so on.
Why is end correction needed?
The vibrating air extends slightly outside each open end, so the effective acoustic length is longer than the physical tube length.
What is the end correction for an open pipe?
A simple estimate is e = 0.6r per open end, where r is the pipe radius. For two open ends, total correction is 2e = 1.2r.
How is an open pipe different from a closed pipe?
An open pipe has both ends open and supports all harmonics. A closed pipe has one closed end and supports only odd harmonics.
Why does a shorter open pipe sound higher?
Shorter length means shorter wavelength. Since f = v / λ, shorter wavelength gives higher frequency and higher pitch.
How does temperature affect open pipe pitch?
Higher temperature increases the speed of sound in air, so the resonant frequency and pitch become slightly higher.