PH 105
Dr. Cecilia Vogel
Lecture 7
OUTLINE
Standing Waves in Tubes
open vs closed
end correction
Modes
fundamental
harmonics
partials
overtones
Resonance
Resonance occurs
when the frequency of the
driving force matches a natural
frequency of the driven system,
& the driving force has a large
effect on the driven system.
Resonance Examples
Recall
for a string fixed at both ends
or a tube with both ends open
or a tube with both ends closed
f1 =
fn=
n =
Longitudinal vs Transverse
Note:
These images are GRAPHS of pressure in tube
They do NOT show air molecule motion
Sound waves are longitudinal waves
means the motion of the medium (air) and
the motion of the wave (sound) are along
the same axis
String waves are transverse waves
means the motion of the medium (string)
and the motion of the wave are
perpendicular
Traveling vs Standing
traveling waves
means the disturbance moves through the
medium at the wave speed.
standing waves
means the nodes and antinodes remain
fixed, do not move through the medium.
standing waves
can be thought of as two traveling waves
traveling in opposite directions
and interfering: constructively at ________,
destructively at _____
Tube with One Closed End
If tube is closed at one end
there is a pressure _________ at that end
_______ at the other end
If
etc
 L =l/4
L =
L =
Resonant Frequencies
L = nl/4
n = 1, 3, 5, 7, 9…. (only odd!)
Since lf = v
v
f n
4L
n odd
f  nf1
Pitch of Tube
Pitch often reflects
compare pitch of open vs closed tube
listen to pitch to determine freq, f1.
Example
Calculate three lowest resonant freq’s
for tube with both ends open
f1 =
f2 =
f3 =
Calculate three lowest resonant freq’s
for tube with one end open
f1 =
f3 =
f5 =
Example
Calculate length of tube with both ends open
f1 = v/2L
 L=
Calculate length of tube with one end open
f1 = v/4L
 L=
End Correction
Actual length is smaller than calculated
because pressure doesn’t equilibrate
pressure varies
as if tube were
For
add an ______________ to the actual length
add
r is
Fundamental
Pitch is often determined by the lowest
resonant frequency of a system:
this is called the
behavior is
If only one frequency involved in a
sound, it’s called a
Partials
Many systems have several
resonant frequencies.
The sound they make is made up of many
The different frequencies that make
up a sound are called
They are numbered from
The 1st partial is the
Harmonics
In some
such as
the frequencies of the partials are multiples
of the

If this is true,
the partials are called
Overtones
The lowest freq partial is the
All other partials are called
“over,”
the 1st overtone is
String Example
__________, ___ partial,
___ harmonic ( _ times f1)
___ overtone, ___ partial,
___ harmonic ( _ times f1)
___ overtone, ___ partial,
___ harmonic ( _ times f1)
Tube Example (one end open)
___________, ___ overtone, ___ overtone,
___ partial,
___ partial,
___ partial,
___ harmonic ___ harmonic
___ harmonic
( _ times f1)
( _ times f1)
Summary
Comparing open and closed pipes
longitudinal vs transverse
traveling vs standing waves
Single freq  pure tone
complex tone made of partials
overtones are partials, excluding
fundamental
harmonics are partials that have
freq=integer*fundamental frequency