Open Pipe Fundamental
Lowest note of a pipe open at both ends (like a flute).
Formula
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Example
L=0.5 m: f = 343/1.0 = 343 Hz
How it works
An open pipe has air that can move freely at both ends, so the ends act like displacement antinodes. The fundamental note is the simplest standing wave that fits one half of a wavelength into the pipe, so the pipe length is L = λ/2, giving λ = 2L and therefore f = v/λ = v/(2L).
When to use it
Use this for the lowest resonant frequency of open-ended tubes such as flutes, organ pipes, or any air column open at both ends. It is also useful when estimating how changing the tube length or temperature will change the pitch.
Worked example, step by step
Suppose an open pipe is 0.80 m long and the speed of sound is 340 m/s. Step 1: Write the formula: f = v / (2L) Step 2: Substitute the values: f = 340 / (2 × 0.80) Step 3: Calculate the denominator: 2 × 0.80 = 1.60 Step 4: Divide: f = 340 / 1.60 = 212.5 Hz Final answer: the fundamental frequency is 212.5 Hz.
Common mistakes to avoid
- Using f = v/L instead of f = v/(2L), which ignores that the fundamental has half a wavelength in the pipe
- Forgetting to convert the pipe length to metres before substituting into the formula
- Using the speed of sound at the wrong temperature, which can shift the frequency noticeably
Did You Know?
A pipe closed at one end sounds an octave lower than an open pipe of the same length.
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