Finding the resonant
frequencies of Acrylic in
the Chladni plate
experiment
Yashovardhan Bagul(02)
Devanshu Ekande(11)
Arnav Kulkarni(17)
Om Shouche(33)
Abstract
The Chladni plate experiment done with an acrylic plate as the resonator, is explored in this
study. Investigating the resonant frequencies of the acrylic plate by vibrating it with a sound
source and visualising the resulting Chladni patterns was set as the objective of this
experiment. In the field of acoustics, the Chladni plate experiment is a classic demonstration,
through which valuable insights into the vibrational behaviour of flat surfaces are provided
when subjected to acoustic stimulation.
The acrylic plate was firmly secured at its centre, and a range of sounds using a subwoofer
were employed to excite the plate's vibrations. Fine powder (Rangoli) was uniformly spread
over the surface to enhance the visualisation of Chladni patterns. These patterns were
observed to emerge at distinct frequencies, reflecting the resonant modes of the acrylic
plate. The locations of nodal lines and the geometric shapes formed by the powder served
as visual representations of the plate's vibrational behaviour.
By systematically varying the frequency of the excitation source, the resonant frequencies of
the acrylic plate were identified, and their corresponding Chladni patterns were documented.
The results of this experiment provide valuable insights into the resonant properties of the
acrylic plate.
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00 | Index
1. Introduction
2. Literature Review
3. Glossary
4. Variable Analysis
5. Aim
6. Experimental Design
7. Data
8. Observations and Conclusion from Data
9. Inferences
10. Result
11. Conclusion
12. References
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01 | Introduction
1) Concept
The speaker generates vibrations. A cone is stuck onto the speaker and a
cardboard sheet is stuck on the cone. So, the cardboard vibrates with the speaker. A
powder(rangoli) is spreaded evenly on the cardboard. The powder then gets
rearranged into patterns. We observed the effect of frequency on the pattern formed.
2) Working Principle
As the nail generates vibrations from the centre of the plate, waves travel
through the plate (the medium), they eventually reflect back from the edges and start
travelling towards the centre. These reflected waves interfere with the initial incoming
waves to form standing waves. That is, waves which are stationary when it comes to
horizontal movement. Here is an image demonstrating the standing wave formed at
some frequency for a metal plate -
Sand tends to settle at areas with zero movement, which are nodes. This ultimately
results in the formation of patterns
3) Our questions
a) How does the wave travel through the plate?
b) What are the resonant frequencies of acrylic?
c) How does frequency affect the number and shape of nodes?
d) How is there a difference between the resonant frequencies of metal and
acrylic?
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02 | Literature Review
➔ The patterns (good ones) are formed only at resonance frequencies.
➔ Meaning of Resonance, Resonant frequencies, Standing waves, etc.
➔ The particles gather around at nodes where the displacement of the plate is zero.
➔ The amplitude of the wave does not change the so formed pattern on the plate, only
changes the time required for it to form.
➔ The patterns formed on the metal plate were referred to.
03 | Glossary
➔ Frequency - the number of cycles or repetitions of the wave per unit of time
➔ Amplitude - The height of the wave measured from the point it intersects the X axis
➔ Interference ◆ Constructive - when the amplitude of the waves increases due to the wave
amplitudes reinforcing each other.
◆ Destructive - when the amplitude of the resulting wave decreases due to the
wave amplitudes cancelling each other out.
➔ Natural frequency - the frequency at which a system tends to oscillate in the absence
of any driving force.
➔ Resonance - the tendency of a system to oscillate with greater amplitude at some
frequencies (also at the natural frequency) than at others
➔ Resonant frequency - The frequency at which resonance occurs
➔ Standing waves - also known as stationary waves, are waves which oscillate in time
but whose peak amplitude profile does not move in space.
➔ Nodes - A point, line or surface of an object which is free/relatively free from
vibrations
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04 | Variable Analysis
Component
Variables
Independent Qualitative/ Physical/ Discrete/Cont
/Dependent Quantitative Chemical inuous
Particulate
Matter
Type of matter
Independent
Qualitative
Chemical
Discrete
Momentum
Dependent
Quantitative
Physical
Continuous
Dependent
Quantitative
Physical
Continuous
Size
Independent
Quantitative
Physical
Continuous
Weight
Independent
Quantitative
Physical
Continuous
Number of types of particles Independent
Quantitative
Physical
Discrete
Ratio of weights of types of
Independent
particles
Quantitative
Physical
Continuous
Moisture
Independent
Quantitative
Physical
Continuous
Magnetic properties
Independent
Qualitative
Physical
Continuous
Density
Independent
Quantitative
Physical
Continuous
Weight
Independent
Quantitative
Physical
Continuous
Area
Independent
Quantitative
Physical
Continuous
Material
Independent
Qualitative
Physical
Discrete
Shape
Independent
Quantitative
Physical
Continuous
Frequency
Independent
Quantitative
Physical
Continuous
Amplitude
(Range
of
movement of diaphragm of Independent
speaker)
Quantitative
Physical
Continuous
Number of speakers
Independent
Quantitative
Physical
Discrete
Symmetry of speakers
Independent
Qualitative
Physical
Continuous
Area of contact with the
Independent
plate
Quantitative
Physical
Continuous
Average frequency of all
Dependent
speakers
Quantitative
Physical
Continuous
Distance travelled
specific grain
Plate
Oscillator
(Speaker)
by
a
5
Additional
Weight
Surrounding
Pattern
Duration
Independent
Quantitative
Physical
Continuous
Periodicity
Independent
Quantitative
Physical
Continuous
Weight
Independent
Quantitative
Physical
Continuous
Location of weight
Independent
Quantitative
Physical
Continuous
Number
Independent
Quantitative
Physical
Continuous
Contact area with the plate
Independent
Quantitative
Physical
Continuous
Volume
Independent
Quantitative
Physical
Continuous
Shape
Independent
Quantitative
Physical
Continuous
Wind speed
Independent
Quantitative
Physical
Continuous
Temperature
Independent
Quantitative
Physical
Continuous
mass of air per set volume
Independent
Quantitative
Physical
Continuous
Number of nodes
Dependent
Quantitative
Physical
Discrete
Type of nodes
Dependent
Qualitative
Physical
Discrete
Equation of node
Dependent
Quantitative
Physical
Continuous
Amount of sand that fell off
Dependent
the setup
Quantitative
Physical
Continuous
Size of nodes
Dependent
Quantitative
Physical
Continuous
Time required for pattern to
Dependent
form
Quantitative
Physical
Continuous
05 | Aim
To find the resonant frequencies of Acrylic plate
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06 | Experimental Design
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Components and their Functions 1.
Amplifier - Controls the amplitude of the wave.
2. Frequency Generator (website) - Changes frequency of the wave.
3. Speaker - Moves up and down (vibrate) at the given frequency.
4. Cone - Transfers the vibrations from the speaker to the nail.
5. Nail - Transfers the vibrations from the cone to the plate.
6. Plate - Vibrates at the given frequency and makes the sand (rangoli) particles jump.
7. This plate must be parallel to the ground, ensuring minimal rangoli falling off.
8. Rangoli - Particles jump up and down till they manage to reach a node where the plate
is stable.
Procedure -
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1.
Obtain a plain plate of any material (we used a square acrylic plate)
2. Make a hole right in its middle, such that a nail/screw will be able to fit in it.
3. Make a hole of the same radius in the centre of the top of a cone.
4. Insert and stick the screw to the plate and cone as can be seen in the image above.
5. Ensuring that the cone has a smooth and even bottom, stick it symmetrically onto the
speaker’s diaphragm.
6. Connect the speaker to a suitable amplifier which is connected to a frequency
generator. (PC in our case)
7. Sprinkle sand evenly onto the plate and experiment with different frequencies.
Experimental Design
Component
Variables(independent)
How to control
Particulate
Matter
Type of matter
Rangoli
Size
By passing through चाळणी, winnowing
Weight
Doesn't affect formation of pattern
Number of types of particles 1; only Rangoli
Ratio of weights of types of
Only one type of particle used at a time
particles
Plate
Moisture
0 moisture, achieved by keeping in
sunlight
Magnetic properties
Removing any magnetic material from
sand with the help of magnet
Density
The same plate will be used during
every reading
Weight
The same plate will be used during
every reading
Area
361 sq. cm. The same plate will be used
during every reading
Shape
Square. The same plate will be used
during every reading
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Speaker
and
generated
Frequency
sound
We will plug in a function generator
into the amplifier which will control the
vibrations
Doesn't affect formation of pattern,
Amplitude
(Range
of needs to be increased for higher
movement of diaphragm of frequencies for the pattern to form in a
speaker)
reasonable amount of time, or for it to
form at all.
Number of oscillators
`1 every time
Threaded rod Symmetry of oscillators w.r.t The source of vibration (nail) will be at
(long screw)
plate
the centre of plate
Area of contact with the Dimensions of the nail will remain
plate
constant.
Additional
Weight
plate
Surrounding
Amplifier
on Mass
Zero weight. No extra weight will be
used.
Location of weight
Zero weight. No extra weight will be
used.
Number
Zero weight. No extra weight will be
used.
Contact area with the plate
Zero weight. No extra weight will be
used.
Volume
Zero weight. No extra weight will be
used.
Shape
Zero weight. No extra weight will be
used.
Wind speed
Fan will be off, expt. in enclosed space
Temperature
Will do the experiment in enclosed
space
Mass of air per set volume
Same room
experiments
Amplitude
Doesn't affect formation of pattern,
needs to be increased for higher
frequencies for the pattern to form in a
reasonable amount of time, or for it to
form at all.
will
be
used
for
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07
|
Data
Here are the frequencies at which we found complete patterns-
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12
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08 | Observations and Conclusions from Data
1.
As the frequency is increased, the pattern complexity increases.
a. The number of nodes increases.
b. The length of nodal lines decreases.
2. As the frequency is increased, the amplitude required for the pattern to form
increases.
a. The plate oscillates violently at lower frequencies.
b. The oscillation of the plate is not very noticeable at higher frequencies ≥ 2000
Hz.
3. The pattern shows a smooth transition if the frequency is changed at a constant rate.
4. The rate of change of pattern decreases at increasing frequency.
5. Antinodes are formed at the centre of the plate and at the edges of the plate at all
frequencies.
6. Increase in amplitude speeds up the process of pattern formation.
7. A similar pattern is observed at least ±10 hz of any frequency.
8. Lighter particles tend to stick to the plate during pattern formation.
9. If a pattern is formed at ‘x’ frequency and we play ‘y’ frequency, the pattern at ‘y’
frequency doesn’t form neatly in some cases, even if ‘x’ and ‘y’ are resonant
frequencies.
10. If we stop the frequency after a pattern has formed and tilt the setup for the sand to
fall, some of it sticks to the plate, showing us the pattern better.
11. The sound that we hear at higher frequencies varies as our position with respect to the
plate changes. At some points it is muffled, while it is clear at the other.
12. We can judge how the cone is stuck based on the pattern i.e. If the cone is loose at
one side, the pattern on that side remains incomplete.
13. The pattern formed at a higher frequency on acrylic is formed at a lower frequency on
metal. The metal plate pattern was seen while reading research papers.
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14. Some of the resonant frequencies that we found were multiples of a lower resonant
frequency.
a. Eg. 135 - 405, 675, 945
15. The quantity of rangoli does not affect pattern formation. It just increases the thickness
of the node.
16. If the rangoli is not sieved, the lighter particles circle around the heavier particles at
nodes.
17. Some particles dance around on antinodes even after pattern formation.
a. The frequency with minimal amount of such particles (ideally zero) is a
resonant frequency.
18. The weight and size of the particles of the rangoli affects the sharpness of the pattern.
a. Lighter and smaller provide less scattered and sharp nodal lines.
09 | Inferences
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●
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Frequency and Pattern Complexity: The increasing complexity of Chladni patterns
with higher frequencies can be attributed to the fundamental vibrational modes of the
plate. At higher frequencies, more modes are excited simultaneously, leading to
intricate patterns.
Frequency and Node Count: Higher frequencies result in more nodes due to the
shorter wavelengths associated with these frequencies. The plate's surface divides
into smaller sections that remain stationary, creating more nodal lines.
Frequency and Nodal Line Length: The inverse relationship between frequency and
nodal line length is a consequence of the wavelength of the sound wave. Higher
frequencies have shorter wavelengths, causing nodal lines to be closer together and
shorter in length.
Amplitude and Pattern Formation: Higher amplitudes are necessary for pattern
formation at higher frequencies because increased energy is required to overcome
damping forces (restrictive forces) and generate more pronounced vibrations at these
frequencies.
Plate Oscillation: The violent oscillation of the plate at lower frequencies is due to the
fact that at these frequencies, the plate is easily excited into large-amplitude motion.
At very high frequencies, damping and energy loss become more prominent, leading
to less noticeable plate oscillation.
Smooth Frequency Transition: A smooth transition of patterns when the frequency
changes at a constant rate occurs because the plate responds gradually to changes
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●
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●
●
in the excitation frequency. This is a result of the plate's ability to smoothly shift
between resonant modes.
Amplitude Impact: Increasing amplitude speeds up pattern formation because it
provides more energy to drive the plate into vigorous motion, allowing patterns to
develop more rapidly.
Pattern Similarity: A certain range of frequencies produces similar patterns because
the plate has multiple resonant frequencies corresponding to different vibrational
modes. Within a small frequency range, these modes may overlap and produce
similar patterns.
Particle Behaviour: Lighter particles may adhere to the plate because of the little
moisture present on the plate.
Rangoli Quantity: The quantity of rangoli does not affect the fundamental structure of
the pattern because it primarily impacts the density of particles at nodes and
antinodes rather than the plate's vibrational modes.
Particle Interaction: Un-sieved rangoli particles exhibit unique behaviour because they
have a wide range of sizes and masses. Lighter particles which do not stick to the plate
can move more easily and circulate around heavier ones at nodal regions.
Minimal Particle Presence: A resonant frequency with minimal or zero particles
dancing around antinodes indicates that the plate's vibrations have reached a
maximum amplitude, causing particles to be displaced from these regions.
Particle Properties: The weight and size of rangoli particles influence the sharpness of
the pattern because lighter and smaller particles are more easily moved by the plate's
vibrations, resulting in clearer and less scattered nodal lines.
10 | Result
➔ Resonant frequencies (in Hz) of our Acrylic plate between 100 Hz and 1200 Hz are◆ 117
◆ 135
◆ 234
◆ 360
◆ 405
◆ 540
◆ 585
◆ 675
◆ 945
◆ 1053
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11 | Conclusion
In this project, we conducted an exploration of the Chladni plate experiment, focusing on the
use of an acrylic plate as the resonator to ascertain its resonant frequencies. The Chladni plate
experiment served as a valuable tool for investigating the vibrational characteristics of flat
surfaces when exposed to vibrations.
Firstly, we successfully observed and documented a range of Chladni patterns on the acrylic
plate, each corresponding to a distinct resonant frequency. The ability to visualise these
patterns was not only educational but also visually appealing.
Secondly, by systematically varying the frequency of the excitation source, we were able to
identify and catalogue the resonant frequencies of the acrylic plate. This data can be used
for understanding the plate's vibrational behaviour.
Moreover, this project reinforced the significance of practical experimentation in the learning
process. It allowed us to apply theoretical knowledge of acoustics and resonance to a realworld scenario, fostering a deeper appreciation for the subject matter.
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12 | References
Introduction to topic:
1) https://www.seattleu.edu/scieng/physics/physics-demos/waves/chladni-plates/
2) https://youtu.be/OLNFrxgMJ6E
Apparatus / Setup:
1) https://www.instructables.com/Mechanical-Wave-Driver-for-Chladni-Plate/
2) https://www.instructables.com/Easy-Chladni-Plate/
3) https://youtu.be/hKmPc0Q0kKg
Theory:
1) https://physics.stackexchange.com/questions/90021/theory-behind-patterns-formedon-chladni-plates
2) Wikipedia sites for term meanings and underlying concepts.
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