FE Physics
Formulas & Explanation     Dutch version

Standing longitudinal waves

Wind instruments and  organ pipes

The same type of calculations

An antinode is created at the mouth of the pipe!

Example 3

Find the frequency of the fundamental of an open organ pipe with a length of 2.0 m

at a temperature of 20 C  (speed of the sound is 343 m/s) Open organ pipe : the open top is also an antinode

Distance from antinode to antinode A-A = ½  λf

So  λf = (2)( 2.0) = 4.0 m

v = 343 m/s

v = ff  λf

343 = ff . 4.0

ff = 85.8 Hz

Example 4

Find now the frequency of the fundamental of a stopped organ pipe with the same length

Fundamental: Stopped organ pipe : the closed top created a node

length pipe  (N-A) = ¼ λ       So  λ= (4)( 2.0) = 8.0 m

v = ff  λf       343 = ff   8.0      ff= 42.9 Hz    ( 2 x lower then the ff  of an open pipe)

Example 5

Calculate the frequency of the second harmonic of a stopped organ pipe with the same length of 2.0 m at the same temperature of 20 C length organ pipe = 2.0 m

length = ¾ λ 1     λ1= 2.67 m

f1 =  128.5 Hz