Energy and Mechanical Waves
AIR COLUMNS
REVIEW OF STANDING WAVES

http://id.mind.net/~zona/mstm/physics/wave
s/standingWaves/understandingSWDia1/Unde
rstandingSWDia1.html

http://www.enm.bris.ac.uk/research/nonlinear
/tacoma/tacnarr.mpg
Harmonics
The frequency of
a vibrating string
is determined by:
 mass of the
string
 length of the
string
 tension in the
string

AIR COLUMNS
There are two types of air columns, open and
closed.
 Closed Air Columns
 ***Only one side of the column is closed***
 When a closed air column "contains" a standing
wave a node and anti -node are present. The
node exists at the closed end and the anti node at the open end. This results in the
following harmonics:

CLOSED AIR COLUMNS
The human vocal cavity (mouth and throat) behaves
exactly as a resonate air column closed at one end, as
shown in the diagram below.
CLOSED TUBES WILL ONLY EVER POSSESS ODD
NUMBERED HARMONICS.
Harm.
#
# of Waves
in Column
# of
Nodes
# of
Antinodes
LengthWavelength
Relationship
1
1/4
1
1
= (4/1)*L
3
3/4
2
2
= (4/3)*L
5
5/4
3
3
= (4/5)*L
7
7/4
4
4
= (4/7)*L
9
9/4
5
5
= (4/9)*L
LENGTH OF A CLOSED AIR COLUMN

In a closed pipe the longest possible resonant
wavelength is four times the length of the pipe
1
L  
4
L  length of air column ( pipe) (m)
  wavelength (m)
OPEN AIR COLUMNS
***Both sides of the column must be open***
 When an opened air column "contains" a
standing wave only anti - nodes are present.
The anti - nodes exist at both of the open ends
of the column. This results in the following
harmonics:

OPEN AIR COLUMNS

In an open pipe,
the longest
possible resonant
wavelength is
twice the length of
the pipe
1
L  
2
L  length of air column ( pipe) (m)
  wavelength (m)
EXAMPLES:
1. A closed air column resonates with a
fundamental frequency of 508 Hz. What is
the length of the air column if the speed of
the sound wave is 523 m/s?
Solve for wavelength.
vf
v

f
523m / s

508 Hz
  1.0295m
1
L 
4
1
L  (1.0295m)
4
L  .257375m  .257m
2. An opened air column resonates with a
fundamental frequency of 607 Hz. If the
length of the air column is 89.3 cm, what is
the speed of the sound?
L  0.5
L

0.5
0.893m

0.5
  1.786m
vf
v  (1.786m)(607 Hz )
v  1.08 10 m
3
ASSIGNMENT: