LESSON 06
Closed Pipe
Standing waves in pipes closed at one end.
Frequency1.00×
Amplitude1.00×
A closed pipe (like a clarinet) has a node at the closed end and an antinode at the open end. Only odd harmonics are possible.
Boundary conditions
Closed end → displacement node. Open end → antinode.
Harmonics
Frequencies: f_n = n·v / (4L), with n = 1, 3, 5, …
Key Formulas
Odd harmonics
fₙ = n·v / (4L)
n odd
Fundamental
f₁ = v / (4L)
low + warm
Real-life applications
- Clarinets
- Test-tube whistles
- Bottle music
Summary
- Closed pipe: only odd harmonics.
- Fundamental is one octave lower than an open pipe of the same length.
Check Yourself
Q1.A clarinet behaves like a…