Name ______________________________
Partner(s) ___________________________
________________________
Date ________________________________
Physics 23 Laboratory
The Speed of Waves on a String
Abstract: The velocity and the uncertainty in velocity of a wave traveling on a string are found by two
different methods. The first method uses the frequency and wavelength of a standing wave, and the
second method uses the tension in the string and the linear density of the string. The values are then
compared with each other. This comparison is performed for three different tensions.
In the first method, one end of a string is attached to a support rod, and the other end passes over
a pulley to a hanging weight. The string passes through a groove in a mechanical oscillator that is placed
close to the support rod, and the oscillator sets the string vibrating. The frequency of the oscillator is
adjusted until standing waves are produced on the string. If the distance from one node to another node
and the number of loops between the nodes are known, then the wavelength of the standing wave can be
2L
calculated. That is,  
, where L is the distance between the nodes and N is the number of loops
N
between the nodes. The speed of the wave is then the product of frequency and wavelength, or
 2L 
v  f  f   .
N
F
. In this case F is the tension in the string

that is produced by the hanging weight, and  is the linear density of the string.
In the second method, the speed of the wave is v 
Diagram:
pulley
L
mechanical
oscillator
v=
F

u=
2Lf
N
m
frequency
generator
In the above diagram, six loops are shown but the length of only four loops is measured because
the position of the nodes at the mechanical oscillator and the pulley cannot be accurately
determined.
Data:
Linear Density of the String, (   g/m: ____________________
100 gram hanging mass data:
Trial
Frequency, (f  f)
(Hz)
L  L
(cm)
Number of Loops, N
L  L
(cm)
Number of Loops, N
L  L
(cm)
Number of Loops, N
1
2
3
150 gram hanging mass data:
Trial
Frequency, (f  f)
(Hz)
1
2
3
200 gram hanging mass data:
Trial
1
2
3
Frequency, (f  f)
(Hz)
Calculations:
1.
100 gram mass calculations:
a.
speed of the wave (v  v) from tension and linear density:
b.
speed of the wave (u  u) from frequency and wavelength:
Trial 1:
Trial 2:
Trial 3:
Average:
2.
150 gram mass calculations:
a.
speed of the wave (v  v) from tension and linear density:
b.
speed of the wave (u  u) from frequency and wavelength:
Trial 1:
Trial 2:
Trial 3:
Average:
3.
200 gram mass calculations:
a.
speed of the wave (v  v) from tension and linear density:
b.
speed of the wave (u  u) from frequency and wavelength:
Trial 1:
Trial 2:
Trial 3:
Average:
Results:
The Results Table
Hanging
mass
Speed from tension and linear
density, v  v,
(m/s)
Average speed from frequency and
wavelength, u  u,
(m/s)
100 g
150 g
200 g
One-dimensional error bar graphs:
100 g mass:
v and u (m/s)
150 g mass:
v and u (m/s)
200 g mass:
v and u (m/s)
Conclusions:
Do the velocity ranges overlap for each value of the hanging mass? If they don’t, then what do you
think is responsible for the lack of the overlap? If there is an overlap, what does the overlap imply?
Explain.
Indicate what you think are the main characteristics of your experiment that contribute to the error.
Explain how these characteristics affect the speed of the wave on the string.