Report #2: Standing Waves
Introduction
The objective of this lab was to analyze how different physical properties of a string
influence its behavior during oscillatory motion, particularly focusing on the formation of
standing waves. Standing waves occur when two waves of equal amplitude and frequency
travel in opposite directions, producing fixed points called nodes—locations where the
amplitude is zero. These nodes help visualize the wavelength and frequency of a wave,
which can be calculated using the equation 𝜆=2𝐿/𝑛, where 𝐿 represents the string length
and 𝑛 the number of nodes. Additionally, wavelength and frequency share an inverse
relationship, as expressed by the equation 𝜆=𝑣/𝑓. By substituting this relationship into the
formula for standing waves, the frequency can be determined as 𝑓=𝑛𝑣/2𝐿. Our hypothesis
posited that increasing the frequency using a wave oscillator would generate more nodes,
signifying the creation of more waves and a reduction in wavelength. To test this
hypothesis, we used a slotted mass set, a wave oscillator unit, a sine wave generator, and a
thick white string, and observed how altering the frequency impacted the number of nodes
and the corresponding wavelength of the standing waves.
Procedure
The experiment began by observing the type of wave produced by the string. The string
was plucked gently, and the resulting wave was identified as a transverse wave, since its
motion was perpendicular to the string’s equilibrium position. This preliminary step
provided a basic understanding of the wave behavior before proceeding to engage the
wave generator.
After determining the wave type, the string was connected to the Sine Wave Generator to
start the experiment officially. The frequency was set initially at around 100 Hz, and the
frequency knobs were slowly adjusted until the first resonance mode, n = 1, was observed.
, Experiment 1: Measurements
This resonance mode appeared as a standing wave with one complete loop, or node,
across the string.
Next, the apparatus was set up by measuring the total length of the string along the track
using a ruler that started at zero. This recorded length, denoted as L (L = 0.985m), was used
for calculations. The string was then securely positioned over the pulley system, with a
mass pan attached to one end and two 100-gram slotted weights added to the pan to
create tension. Ensuring that the string was properly aligned and taut was essential before
proceeding to further wave generation.
Following the identification of the first resonance mode, data collection proceeded by
further adjusting the frequency to identify additional resonance modes, corresponding to n
= 1, 2, 3, 4, and 5 . Each subsequent resonance mode displayed an additional node, with n =
2 showing two loops and n = 5 exhibiting five distinct loops. For each resonance mode, the
corresponding frequency and wavelength (lambda) were recorded in a data table.
After collecting the data, the recorded values were used to create a graph in Excel. The
vertical axis of the plot represented 1/n, while the horizontal axis depicted lambda. This
graph was used to verify the theoretical relationship between these variables, expressed by
the formula 1/n = 1/2L*𝜆. The slope of the resulting line should be equal to 1/2L, and this
was confirmed by analyzing the graph. Any deviations from this expected slope were
considered and discussed in the context of experimental errors or limitations.
The experiment concluded by verifying that the plotted data were consistent with the
theoretical wave relationships for a string under tension. By comparing the slope of the line
to the theoretical value using the measured length L of the string, the accuracy and
reliability of the experimental data were validated, confirming the theoretical principles of
wave behavior in a vibrating string.
Results/Data/Calculations
Warm Up Exercise:
Type of wave: Transverse
2
Introduction
The objective of this lab was to analyze how different physical properties of a string
influence its behavior during oscillatory motion, particularly focusing on the formation of
standing waves. Standing waves occur when two waves of equal amplitude and frequency
travel in opposite directions, producing fixed points called nodes—locations where the
amplitude is zero. These nodes help visualize the wavelength and frequency of a wave,
which can be calculated using the equation 𝜆=2𝐿/𝑛, where 𝐿 represents the string length
and 𝑛 the number of nodes. Additionally, wavelength and frequency share an inverse
relationship, as expressed by the equation 𝜆=𝑣/𝑓. By substituting this relationship into the
formula for standing waves, the frequency can be determined as 𝑓=𝑛𝑣/2𝐿. Our hypothesis
posited that increasing the frequency using a wave oscillator would generate more nodes,
signifying the creation of more waves and a reduction in wavelength. To test this
hypothesis, we used a slotted mass set, a wave oscillator unit, a sine wave generator, and a
thick white string, and observed how altering the frequency impacted the number of nodes
and the corresponding wavelength of the standing waves.
Procedure
The experiment began by observing the type of wave produced by the string. The string
was plucked gently, and the resulting wave was identified as a transverse wave, since its
motion was perpendicular to the string’s equilibrium position. This preliminary step
provided a basic understanding of the wave behavior before proceeding to engage the
wave generator.
After determining the wave type, the string was connected to the Sine Wave Generator to
start the experiment officially. The frequency was set initially at around 100 Hz, and the
frequency knobs were slowly adjusted until the first resonance mode, n = 1, was observed.
, Experiment 1: Measurements
This resonance mode appeared as a standing wave with one complete loop, or node,
across the string.
Next, the apparatus was set up by measuring the total length of the string along the track
using a ruler that started at zero. This recorded length, denoted as L (L = 0.985m), was used
for calculations. The string was then securely positioned over the pulley system, with a
mass pan attached to one end and two 100-gram slotted weights added to the pan to
create tension. Ensuring that the string was properly aligned and taut was essential before
proceeding to further wave generation.
Following the identification of the first resonance mode, data collection proceeded by
further adjusting the frequency to identify additional resonance modes, corresponding to n
= 1, 2, 3, 4, and 5 . Each subsequent resonance mode displayed an additional node, with n =
2 showing two loops and n = 5 exhibiting five distinct loops. For each resonance mode, the
corresponding frequency and wavelength (lambda) were recorded in a data table.
After collecting the data, the recorded values were used to create a graph in Excel. The
vertical axis of the plot represented 1/n, while the horizontal axis depicted lambda. This
graph was used to verify the theoretical relationship between these variables, expressed by
the formula 1/n = 1/2L*𝜆. The slope of the resulting line should be equal to 1/2L, and this
was confirmed by analyzing the graph. Any deviations from this expected slope were
considered and discussed in the context of experimental errors or limitations.
The experiment concluded by verifying that the plotted data were consistent with the
theoretical wave relationships for a string under tension. By comparing the slope of the line
to the theoretical value using the measured length L of the string, the accuracy and
reliability of the experimental data were validated, confirming the theoretical principles of
wave behavior in a vibrating string.
Results/Data/Calculations
Warm Up Exercise:
Type of wave: Transverse
2
