The Organ Pipe
 During
the last two labs you explored
the superposition of waves and standing
waves on a string.
 Just
as a reminder, when two waves or
more occupy the same region of a
medium at the same time, they will
interfere with each other.
 Today
you continue to study
interference by looking at standing
waves in organ pipes.
Standing Waves

When two sets of waves of equal amplitude
and wavelength pass through each other in
opposite directions, it is possible to create
an interference pattern that looks like a
wave that is
“standing still.”


It is a changing interference pattern.
Today you will create such patterns in open
and closed organ pipes.
Longitudinal Standing Waves
In
Closed Organ Pipes
 When
sound waves pass down a closed
pipe and reflect from the other end, you
have a situation in which two waves are
traveling in opposite directions and
occupying the same region of space at
the same time.
 Under the proper conditions a
longitudinal standing wave can be
established with an antinode at the open
end and a node at the closed end.
 URL
- Animated Organ Pipe
(execute file tube15d.exe or click here (exe) for alternative)
 Again
the lowest frequency standing
wave that can be established is called
the first harmonic.
 Its standing wave pattern looks like
this. (Plotted as displacement of air
molecules versus position in the tube.)
First Harmonic
Fundamental
 This
frequency is also called the
fundamental.

The next higher frequency standing
wave pattern looks like the following.
Third Harmonic
First Overtone
Since this frequency is three times the
first harmonic, it is referred to as the
third harmonic.
 Since this frequency is the next higher
frequency, it is called the first overtone.
(It is the first tone above the
fundamental.)


The next higher frequency standing wave
pattern looks like the following.
Fifth Harmonic
Second Overtone
Since this frequency is five times the first
harmonic, it is referred to as the fifth
harmonic.
 Since this frequency is the next higher
frequency occurring in the pipe, it is called the
second overtone.
(It is the second tone above the fundamental.)

Longitudinal Standing Waves
In
Open Organ Pipes
 When
sound waves pass down an open
pipe and reflect from the other end,
you again have a situation in which
two waves are traveling in opposite
directions and occupying the same
region of space at the same time.
 Under the proper conditions a
standing wave can be established with
an antinode at each end.
URL
- Animated Organ Pipe
(execute file tube15d.exe or click here (exe) for alternative)
 Again
the lowest frequency standing
wave that can be established is called
the first harmonic.
 Its standing wave pattern looks like
this. (Plotted as displacement of air
molecules versus position in the tube.)
First Harmonic
Fundamental
 This
frequency is also called the
fundamental.

The next higher frequency standing
wave pattern looks like the following.
Second Harmonic
First Overtone
Since this frequency is twice the first
harmonic, it is referred to as the second
harmonic.
 Since this frequency is the next higher
frequency, it is called the first overtone.
(It is the first tone above the
fundamental.)


The next higher frequency standing wave
pattern looks like the following.
Third Harmonic
Second Overtone
Since this frequency is three times the first
harmonic, it is referred to as the third
harmonic.
 Since this frequency is the next higher
frequency occurring in the pipe, it is called the
second overtone.
(It is the second tone above the fundamental.)

 In
the experiment today you will
determine the lengths of pipe
necessary to create different
standing wave patterns.
 You will also discover that a
particular frequency will be a first
harmonic for one length of pipe and
yet a different harmonic for a
different length pipe.
 The next two slides will illustrate
this.
Consider a standing wave in a closed organ pipe.
First Harmonic Third HarmonicFifth Harmonic
For this length pipe
the fundamental
would look like this.
Since the wavelength of the
“black” wave is 1/3 the
wavelength of the maroon wave,
the frequency of the black wave
Fundamental First OvertoneSecond Overtone is three times the frequency
of the maroon wave.
Keeping the same frequency but making the pipe three times longer
Keeping the same frequency but making the pipe five times
the original length
This shows that a particular frequency can be a first harmonic for one
pipe, a third harmonic for a longer pipe and a fifth harmonic for an even
longer pipe.
Consider a standing wave in an open organ pipe.
Third Harmonic
First Harmonic
Second Harmonic
Fundamental
First Overtone
Second Overtone
Keeping the same frequency but making the pipe two times longer
Keeping the same frequency but making the pipe three times
the original length
This shows that a particular frequency can be a first harmonic for one
pipe, a second harmonic for a longer pipe and a third harmonic for an even
longer pipe.
 In
this experiment you will need to
calculate the wavelength of a wave
based on knowing the speed and
frequency.
 Remember that
or
v =l f
v
l=f