1
Experiment 2: Standing Waves
Introduction:
From the physical waves we see in the ocean to the invisible waves that help us see and
hear in our daily lives, waves are no doubt a very integral part of our world. There are two types
of waves: transverse and longitudinal waves. Transverse waves look like ocean waves while
longitudinal waves operate via compressions and rarefactions as in sound waves. In general, a
transverse wave is defined as a wave in which the direction of displacement is perpendicular to
its direction of travel. Our focus in this lab are transverse waves, or more specifically, standing
transverse waves.
Standing waves are waves created by vibrations that allow waves to remain “standing” at
certain sections of the string. Because of this, there will be points on the string that will remain
completely still called “nodes.” By analyzing transverse waves as they appear on a string, we
will be able to investigate how the physical properties of a string such as length affect its
behavior, in terms of wavelength and frequency, while undergoing oscillatory motion.
Procedure:
First, as a warmup, a string was held until it was barely taut and plucked to observe the
wave formed by the movement.
For Experiment 1, equipment including a string tied to a frequency generator and weight
attached to a pulley was set up and used as shown in Figure 2. The string was set up so that two
100 g weights were placed at the pulley end of the string. To conduct the experiment, the remote
controlling the frequency generator was turned on and the frequency knobs were adjusted till
frequency resonance and a single antinode, n = 1, was observed. The frequency necessary to
achieve n = 1 was noted down and the wavelength of the wave was measured. This same process
, 2
was repeated four more times to find the frequencies at which two, three, four, and then five
antinodes could be observed. Their respective wavelengths were measured as well.
Finally, a table was constructed to represent the respective wavelengths and frequencies
achieved at each antinode. A scatterplot was created to represent this relationship as well.
Data:
Table 1: The relationship between the frequency of a wave and the number of antinodes and
wavelengths produced.
Number of antinodes, n Wavelength, λ (m) Frequency, f (Hz)
1 2.12 15
2 1.06 31
3 0.71 45
4 0.53 60
5 0.42 74
Relationship Between 1/n and Wavelength
1.4
1.2
1
0.8
1/n
y = 0.4717x - 2E-16
0.6
R² = 1
0.4
0.2
0
0 0.5 1 1.5 2 2.5
Wavelength (λ)
Figure 1. Scatter Plot of the relationship between wavelength, λ (horizontal axis) and 1/n
(vertical axis). Equation of the plot is y = 0.4717x – 2E-16.
Experiment 2: Standing Waves
Introduction:
From the physical waves we see in the ocean to the invisible waves that help us see and
hear in our daily lives, waves are no doubt a very integral part of our world. There are two types
of waves: transverse and longitudinal waves. Transverse waves look like ocean waves while
longitudinal waves operate via compressions and rarefactions as in sound waves. In general, a
transverse wave is defined as a wave in which the direction of displacement is perpendicular to
its direction of travel. Our focus in this lab are transverse waves, or more specifically, standing
transverse waves.
Standing waves are waves created by vibrations that allow waves to remain “standing” at
certain sections of the string. Because of this, there will be points on the string that will remain
completely still called “nodes.” By analyzing transverse waves as they appear on a string, we
will be able to investigate how the physical properties of a string such as length affect its
behavior, in terms of wavelength and frequency, while undergoing oscillatory motion.
Procedure:
First, as a warmup, a string was held until it was barely taut and plucked to observe the
wave formed by the movement.
For Experiment 1, equipment including a string tied to a frequency generator and weight
attached to a pulley was set up and used as shown in Figure 2. The string was set up so that two
100 g weights were placed at the pulley end of the string. To conduct the experiment, the remote
controlling the frequency generator was turned on and the frequency knobs were adjusted till
frequency resonance and a single antinode, n = 1, was observed. The frequency necessary to
achieve n = 1 was noted down and the wavelength of the wave was measured. This same process
, 2
was repeated four more times to find the frequencies at which two, three, four, and then five
antinodes could be observed. Their respective wavelengths were measured as well.
Finally, a table was constructed to represent the respective wavelengths and frequencies
achieved at each antinode. A scatterplot was created to represent this relationship as well.
Data:
Table 1: The relationship between the frequency of a wave and the number of antinodes and
wavelengths produced.
Number of antinodes, n Wavelength, λ (m) Frequency, f (Hz)
1 2.12 15
2 1.06 31
3 0.71 45
4 0.53 60
5 0.42 74
Relationship Between 1/n and Wavelength
1.4
1.2
1
0.8
1/n
y = 0.4717x - 2E-16
0.6
R² = 1
0.4
0.2
0
0 0.5 1 1.5 2 2.5
Wavelength (λ)
Figure 1. Scatter Plot of the relationship between wavelength, λ (horizontal axis) and 1/n
(vertical axis). Equation of the plot is y = 0.4717x – 2E-16.
