Phy 212: General Physics II Lab
Instructor: Tony Zable
page 1 of 3
Experiment: Standing Waves in a String
Objectives:
 To explore the relationship between tension and wavelength for a standing wave in a
string
 To measure the linear density for length of
string
loop
½
node
Introduction
Many fairly common musical instruments are of
a string type. The vibration of the string creates
the note, which may be tuned by adjusting the
tension in the string. The vibration is in the form
of a standing wave, which may be considered as
the superposition of two waves of the same
frequency propagating in opposite directions.
The purpose of this exercise is to investigate the
relationship between the tension in the string
and the wave propagation velocity.
The equipment you will be using consists of a string, one end passing over a pulley; weights
hung from the end of the string produce the tension. At the other end, the string is attached to
the steel reed of an electric vibrator driven by the 60 Hz (110 V) power source. At each half
cycle, as the current reaches a maximum, the reed is attracted to the electromagnet, thus
producing vibrations with a frequency of 120Hz.
The vibration of the reed causes a transverse wave to travel down the string, which is reflected
at the pulley and returns to the reed. The motion of the string is thus a superposition of waves
of identical wavelength traveling in each direction. The phases of the forward and backward
waves are such that there is a cancellation of the transverse string motion every half wavelength
(nodes) and a strong reinforcement of the motion at intermediate positions (loops). This string
pattern is known as a stationary (or standing) wave. When the velocity of propagation is just
right, a wave will travel down and back in the same time that it takes the reed to make an
integral number of complete cycles. When this occurs, the standing waves are intensified so that
they become clearly visible along the string.
The propagation velocity v depends on the linear mass density, or mass per unit length, of the
string () and the tension in the string (FT), according to the relation:
v=
FT

Using the basic relationship between frequency (f), wavelength () and velocity, it is possible to
obtain a relationship which expresses the tension in the string in terms of the wavelength of the
standing waves:
FT
v =  f =
or,



FT =  f 2  2
Phy 212: General Physics II Lab
Instructor: Tony Zable
page 2 of 3
where f = 120 Hz (for the electric vibrator). Note that the above equation is a linear function
between FT and 2. The best-fit slope of the FT vs.
linear mass density for the string.
2 graph should allow you to determine the
Procedure
1. Set-up and clamp down a string vibrator. Clamp down a pulley to the opposite end of the lab
table.
2. Obtain a length of string long enough to attach to the electric vibrator and hang over the
pulley. Measure the mass and length of the string.
Mass:
___________
Length:
___________
3. Attach the string to the reed then attach a hanging mass holder to the opposite end. Hang
this end over the pulley.
4. By adding weight to the weight hanger, vary the tension in the string and obtain a stable
standing wave in the string. Use a meter stick to measure the wavelength and record this value
along with the hanging mass weight. Note: the weight hanger has a mass of 50 g.
5. Repeat step 3 by systematically increasing the string tension. You can stop when you
achieve only 1 or 2 nodes in the string (you don’t want to break the string…)
6. Repeat steps 4 & 5 in reverse by decreasing the tension in the string. This will control for the
effects of stretching in the string.
Trial
Tension force,
FT (N)
Wavelength,
(m)

2

avg =
 =
Wave Speed, v
(m/s)
Phy 212: General Physics II Lab
Instructor: Tony Zable
page 3 of 3
Analysis
1. Calculate 2 for your trials. Does FT appear to vary linearly with 2?
2. Calculate  for each of your trials and record values in the data table.
3. Using the values in the data table, calculate the average and uncertainty for . Use the minmax method to calculate .
4. Using Graphical Analysis, create a graph of FT vs 2. Using the Curve Fit tool, obtain the
slope of the linear best-fit line for your graph. Use this value to estimate the linear mass density
for the string.
Slope of graph: ___________
from graph = ___________
5. Obtain the uncertainty (standard deviation) for the slope. To do this:

Right-click on the fit “Linear Fit for: Data Set … ” object in the graph window

Select “Linear Fit Helper Options”

In the Linear Fit Options window, under Standard Deviations, check the “Slope” box. Then
select “Okay”.
The curve fit parameters will now display the standard deviation for the slope.
Uncertainty of slope: __________
from graph = ___________
6. Calculate the linear mass density () for the string using the above mass and length values.
direct measurement = ___________
7. Do your estimated values for  agree with direct measurement within the limits of the
experimental uncertainty?
8. Which of the above approaches, average calculation or graphical analysis, best agrees with
the direct measurement of  in step 6?
9. Compare the experimental values for . Calculate the % Error for both the average
calculation and graphical analysis approach with the direct measurement.
% Error (calculation):
___________
% Error (graph):
___________