The Vibrating String

During the last lab you explored the superposition
of waves.

When two waves or more occupy the same region
of a medium at the same time, they will interfere
with each other.

In the last lab you learned about constructive
interference, destructive interference, and
partially constructive interference.

Today you will continue to study interference by
looking at standing waves on a string.
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 on a
vibrating string.
Parameters of a Standing Wave
l
There is no vibration at a node.
There is maximum vibration at an antinode.
l is twice the distance between successive
nodes or successive antinotes.
When you pluck a stringed musical
instrument, the string vibration is
composed of several different standing
waves.
 The lowest frequency carried by the
string is called the first harmonic.
 Its standing wave pattern looks like
this.

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 appearing on the string, 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 appearing on the string, it is called
the second overtone.
(It is the second tone above the fundamental.)

In the experiment today you will adjust
the tension in a vibrating string so that you
create different standing wave patterns.
(Adjusting the tension in the string
changes the speed of the wave.)
 Important Note:
The frequency of vibration on your string
will remain constant.
By changing the wave speed you will be
changing the wavelength and therefore the
harmonic number of the standing wave.

To show this let’s put a first harmonic on the string.
First Harmonic
Fundamental
Second Harmonic
First Overtone
Next let’s loosen the string which will slow
the wave down yielding a shorter wavelength.
Slides 11-13 need more work on the language
Third Harmonic
Second Overtone
Loosening the string some more results in an
even shorter wavelength.
Thus your frequency of vibration will be a
first harmonic for a high tension in the
string and different harmonics for lesser
tensions.
 URL
- Animated Vibrating String
(execute file strg15d.exe or click here (exe) for alternative)
Note that a more accurate method of
obtaining the frequency of a standing
wave on a string could be accomplished
by using a strobe light to make the wave
appear to be “standing still.”
 All you would have to do is read the
frequency from the variable frequency
strobe light.

The lab assistant will now give you an
overview of the experimental apparatus
The electric oscillator is located here.
Masses are added here.
When the apparatus is turned on and with the proper
mass on the hanger, standing waves can occur.
This is considered to be one segment.
Points of no vibration are called nodes.
Three are shown here. (Where are they?)
The large vibration areas are called antinodes.
Antinodes
Node
One Segment
Electric Oscillator
Hanger and Masses
By varying the mass on the mass hanger
one can create standing waves with
differing numbers of segments.