PHYSICS EXPERIMENTS — 132
3-1
Experiment 3
Vibrating Strings
In this experiment you shake a stretched flexible
string. When you shake rhythmically at the correct
frequency, the string forms a large standing wave
pattern. The vibrating string resonates at these
frequencies, which are determined by the properties
of the system. You use your observations to
determine the wave speed on the string.
Preliminaries.
This experiment investigates the resonance
conditions of a simple system consisting of a taut
cord fixed at the ends and connected to an external
driving mechanism.
Standing waves will be produced when the
length of the cord is an integral number n of half
wavelengths,
L = n( ln 2)
(eq. 1)
where n is any positive integer and n is the
corresponding wavelength, as shown in Figure 2
(for n = 4). The wave speed v can be related to the
frequencies fn at which resonance occurs,
v =  n fn
(eq. 2)
L
m
FT
Figure 1. Schematic for Standing Waves Experiment
Waves travel back and forth along the cord when
excited by the driver. A standing wave can be
produced by waves of the same frequency traveling
in opposite directions on the cord. The required
driving frequencies are determined by the properties
of the string; the tension FT, the string mass m and
the string length L. When a resonant frequency is
used to drive the string, the maximum amplitude of
vibration of the string will be much larger than the
amplitude of the vibration of the driver and is easily
seen. The standing wave pattern is fixed in space,
as shown in Figure 2. The points which remain
stationary are called nodes, while the points which
undergo maximum oscillation are called antinodes.
node
antinode
Figure 2. Example of a Standing Wave Pattern
The wave speed v depends only on the linear
mass density  of the string ( = m/L, m is the mass
of the string) and the tension FT in the string by
v = FT / m
(eq. 3)
Eq. 2 allows an experimental determination of
wave speed by observation of standing waves. Eq.
3 allows an independent calculation of the wave
speed from the measured properties of the string.
Procedure.
 Select a bungee cord. Measure and record its
mass.
PHYSICS EXPERIMENTS –132
 Hook the bungee cord at one end over the stand
and stretch the other end using the force scale until
the tension force read on the scale is about 5-6 N.
Measure and record the tension and the cord length.
 Clip the speaker clip to the cord near one end.
Adjust the frequency on the driving audio generator
to produce a standing wave. The amplitude
(volume) does not need to be turned up very high.
Setting it too high may damage the speaker!! At
resonance (when the frequency is equal to one of the
frequencies that gives standing waves) the
amplitude of the waves will be larger than for
nearby frequencies and the nodes should be quite
distinct. Vary the frequency to find the largest
amplitude. Record the resonance frequency fn , the
number of antinodes n, and the average distance
between nodes.
3-2
1. Take your resonant frequencies and divide each
by the corresponding number of antinodes. Is there
a pattern? What is its significance?
2. Does your data form a straight line on the graph
of wavelength vs. frequency? Should it?
3. What value do you determine experimentally for
the wave speed? What is the percent difference of
this value from the theoretical value?
4. Suppose you redo the experiment with the same
cord pulled to a longer length. Explain how the
following quantities change: string tension, mass
density, wave speed, wavelengths of standing
waves, frequencies of standing waves. How would
the graph of reciprocal wavelength on the vertical
axis and frequency on the horizontal axis change?
rev. 8/13
 Calculate the wavelength from the average
distance between nodes.
 Look for at least four other resonant frequencies.
Record the frequency and the wavelength for each
standing wave.
 Graph the data with the "wavelength" on the
vertical axis and "frequency" on the horizontal axis.
 Make another graph with "wavelength" on the
vertical axis and "inverse frequency" on the
horizontal axis. Eq. 2 predicts that the data on this
graph should lie on a straight line. Calculate the
wave speed from the slope of the graph.
 Calculate the wave speed from the properties of
the stretched string, using eq 3.
 The experimental calculation of wave speed (from
the graph) should agree with the theoretical
determination of the wave speed (from eq 3.).
Determine the percent difference of the
experimental value from the theoretical value.
Questions (Answer clearly and completely).