Resonance Frequency Calculator Formula

Understand the math behind the resonance frequency calculator. Each variable explained with a worked example.

Formulas Used

Open Pipe Frequency

open_freq = harmonic * sound_speed / (2 * pipe_length)

Closed Pipe Frequency (odd n)

closed_freq = harmonic * sound_speed / (4 * pipe_length)

Variables

VariableDescriptionDefault
harmonicHarmonic Number (n)1
sound_speedSpeed of Sound(m/s)343
pipe_lengthPipe Length(m)0.5

How It Works

Resonance in Pipes

Standing waves form in pipes at specific frequencies determined by the pipe length and boundary conditions.

Open Pipe (both ends open)

f_n = n * v / (2L) where n = 1, 2, 3, ...

Closed Pipe (one end closed)

f_n = n * v / (4L) where n = 1, 3, 5, ... (odd harmonics only)

Worked Example

Fundamental frequency of a 0.5 m open pipe at 343 m/s.

harmonic = 1sound_speed = 343pipe_length = 0.5
  1. 01f_open = n * v / (2L)
  2. 02f_open = 1 * 343 / (2 * 0.5)
  3. 03f_open = 343 Hz
  4. 04f_closed = 1 * 343 / (4 * 0.5)
  5. 05f_closed = 171.5 Hz

Ready to run the numbers?

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