Nova Southeastern University Nova Southeastern University
NSUWorks NSUWorks
Physics Lab Experiments with Simulated Data
for Remote Delivery
Department of Chemistry and Physics
1-2022
Experiment 1.10: Standing Waves on Strings Experiment 1.10: Standing Waves on Strings
Diego Castano
Nova Southeastern University
, [email protected]
Follow this and additional works at: https://nsuworks.nova.edu/physics_labs
Part of the Physics Commons
This Book has supplementary content. View the full record on NSUWorks here:
https://nsuworks.nova.edu/physics_labs/2
Recommended Citation Recommended Citation
Castano, Diego, "Experiment 1.10: Standing Waves on Strings" (2022).
Physics Lab Experiments with
Simulated Data for Remote Delivery
. 2.
https://nsuworks.nova.edu/physics_labs/2
This Book is brought to you for free and open access by the Department of Chemistry and Physics at NSUWorks. It
has been accepted for inclusion in Physics Lab Experiments with Simulated Data for Remote Delivery by an
authorized administrator of NSUWorks. For more information, please contact [email protected].
I. EXPERIMENT 1.10: STANDING WAVES ON STRINGS
A. Abstract
Waves on a string under tension and …xed at both ends result in well-de…ned modes of
vibration with a spectrum of frequencies given by the formula below
B. Formulas
f
n
= n
v
2L
; n = 1; 2; 3; : : : (1)
v =
s
T
(2)
where f
n
is the frequency of the n
th
standing wave mode on the string of length L, linear
mass density , and under tension T , and v is the wave speed on the string.
C. Description and Background
FIG. 1. Standing wave set-up.
The …gure above shows the experimental set-up. An electro-mechanical device vibrates
the end of a string of length, L, under tension. The tension is created by a weight, T = Mg,
hanging over a pulley. The frequency of vibration is adjusted until an identi…able mode of
standing wave is realized. In the …gure, the mode has n = 4 anti-nodes (locations of large
amplitude). In the experiment, this parameter will be …xed.
1
A sample segment of length, `, and mass, m, is used to determine the linear mass density
of the string, = m=`. By combining Eqs. (1) and (2), one can derive the following relation
between f
2
n
and M
f
2
n
=
n
2
g
4L
2
M (3)
In the experiment, the hanging mass is varied, and the frequency associated with n = 4
anti-nodes is determined experimentally. The data collected can then be analyzed. If the
procedure is repeated numerous times, a linear regression analysis can be done and the slope,
&, of the best …t line to f
2
n
vs. M will equal
& =
n
2
g
4L
2
=
4g
L
2
(4)
Because of the presence of g in this equation, it provides an indirect method of determining
the acceleration due to gravity.
2
D. Procedure
1. Measure the length, `, and mass, m, of a sample piece of string from the experiment.
2. Measure the length of the string (from vibrator to pulley), L, used to support the
standing waves.
3. Attach a weight to the end of the string that hangs over the pulley.and record its mass,
M, in the measurement table.
4. Adjust the frequency of the sine wave generator so that a standing wave is set up with
n = 4 anti-nodes. Record this frequency (f
n
) in the measurement table.
5. Repeat steps 3 and 4 four more times with other weights.
3
E. Measurements
sample string mass, m [ gram ]
sample string length, ` [ cm ]
length of string under tension, L = [ cm ]
Trial M [gram] f
4
[Hz]
1
2
3
4
5
4
F. Instructions
1. Calculate the linear mass density of the string sample, .
2. Use the data and the equation for g implied by (4),
g =
L
2
f
2
4
4M
to complete the Plotting Table.
3. Use the Excel …le provided, StandingWavesLabPlot, to plot f
2
4
vs.M (include the
point (0; 0) in the plot), and submit the plot as part of your work.
4. Use the slope, &, of the regression line to determine the acceleration due to gravity,
g
slope
.
5. Based on the results in the table, what is g?
6. Determine the associated standard error, g.
7. What is the percent di¤erence between g and g
slope
?
8. During the semester, you have performed four experiments that either determined the
acceleration due to gravity or whose results could have been used to determine it: The
sphere drop, the inclined air-track and glider, the pendulum, and now standing waves
on a string. Compare these four methods and make a case for which one is optimal if
you conclude there is such a one.
5
G. Calculations
Plotting Table
M [ kg ] f
2
4
[ Hz
2
] g [ m=s
2
]
0 0 N/A
= m=` [ kg=m ]
f
2
4
vs. M: slope, & [ Hz
2
=kg ]
g
slope
[ m=s
2
]
g [ m=s
2
]
g [ m=s
2
]
%-Di¤ (g; g
slope
)
Answer to 8 above:
6