Waves
Standing Wave (Closed Pipe)
Resonant frequencies for pipe closed at one end.
Variables
fnHz
Resonant frequency
Odd harmonics only
In SI units: 1/s
Allowed values: greater than 0
nunitless
Harmonic number
Odd integers 1, 3, 5...
Allowed values: greater than 0, odd whole number
vm/s
Sound speed
In the pipe
Allowed values: greater than 0
Lm
Pipe length
Closed at one end
Allowed values: greater than 0
Derivation
Node at closed end, antinode at open: λ_n = 4L/n (odd n).
Your notes
0/5000
Check value
Round inputs run through this page's calculator. Use it to test your own working or a rearranged form. It is a test case, not a real-world example.
- n = 3 (Harmonic number)
- v = 4 m/s (Sound speed)
- L = 5 m (Pipe length)
Result: fn = 0.6 Hz
Other waves formulas with the same quantities
- Standing Wave on String (Superposition) shares Resonant frequency, Harmonic number
- Speed of Sound in Gas (Sound Waves) shares Sound speed
Where this formula is listed
- Waves formulas, under Superposition.
- In the waves list it comes after Standing Wave (Open Pipe).
- Waves formula sheet, one of 37 formulas printed with symbol keys and SI units.
- The full formula index, grouped by category and topic.
Common questions
What is the Standing Wave (Closed Pipe) formula?
Standing Wave (Closed Pipe) is written f_n = nv/(4L). Resonant frequencies for pipe closed at one end. It belongs to Waves, under Superposition.
What are the units in f_n = nv/(4L)?
In SI units, f_n is resonant frequency, measured in 1/s; n is harmonic number (dimensionless); v is sound speed, measured in m/s; L is pipe length, measured in m.
How is the Standing Wave (Closed Pipe) formula derived?
Node at closed end, antinode at open: λ_n = 4L/n (odd n). The result is f_n = nv/(4L).