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Visualizing Sound Waves Using Chladni Plates

Abstract

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Introduction

Chladni plates, created by German physicist Ernst Chladni in 1787, are used to create a visual representation of sound waves. A source of sound (either a speaker or some kind of instrument) is used to vibrate a medium which has a liquid or grains of solid covering the surface. The vibrations at different frequencies create specific nodal lines on the plate, meaning the plate vibrates a lot in some places and not at all in others. The material resting on the surface moved from areas of high vibration to low vibration, making a specific pattern and creating visual representations of the effects of the sound frequency. By creating and experimenting with Chladni plates, can we investigate how the patterns created change depending on the frequencies at which the sound is played? And can we predict the patterns created by the Chladni plates?

Background

Work with Chladni plates in this experiment requires understanding of sound waves and sinusoidal functions. First and foremost, we must understand what Chladni plates are. They are defined to be plates that are vibrated due to a speaker or instrument. The surface of the plate oscillates in a particular mode of vibration, whose nodes and antinodes form patterns over its surface. The positions of these nodes and antinodes can be seen by sprinkling sand or water upon the plates.

Vibration waves:

In order to make the plate vibrate, a speaker must create changes in the air molecules around the plate. A speaker with a diaphragm creates longitudinal waves, waves that vibrate the particles of the medium in the direction of the line of advance of the wave. This disruption in the air around the speaker moves the water resting in the container as well, creating patterns on the surface.

Figure 1: Longitudinal and transverse waves diagram.

Nodal lines:

The patterns created on the surface of every Chladni plate are due to the nodal lines formed at certain frequencies. On a two dimensional surface, nodal lines, lines where the surface remains motionless, divide the surface of a medium into separate regions vibrating with opposite phases.

Figure 2: A representation of nodes and antinodes on a standing wave.

Figure 3: An example of a Chladni plate model. The red and blue areas represent the antinodes where the plate vibrates the most and the amplitude of the standing wave is maximum or maximum. The white lines areas are the nodes (or nodal lines), the places where the amplitude is zero. The sand or water resting on the surface of the Chladni plate would move away from the blue and red areas and will collect on the white lines.

Resonant frequencies:

Every object has a natural frequency. The natural resonant frequency is the frequency at which a system tends to oscillate in the absence of any driving or damping force. When a Chladni plate is excited/ vibrated at its natural frequency, the pattern created on the plate will be much clearer than when vibrated at another frequency.

Figure 4: An example of one type of Chladni plate, where metal surfaces of different shapes are covered in sand and excited using a violin bow.

Figure 5: Another example of a Chladni plate. A container of water rests on a speaker and a pattern is created in the ripples due to the vibrations from the speaker.

Methods and Materials

In this experiment, I studied the waves created in a container of water when the container rested upon a speaker with a diaphragm and the speaker played sounds of varying frequencies.

Testing for this experiment requires:

a 13.6cm by 13.6cm square plastic dish
10 mL of tap water
A function generator (a piece of electronic test equipment or software used to generate different types of electrical waveforms over a wide range of frequencies)
A speaker with a diaphragm (I used a bookshelf speaker)
Camera/ iPhone to record results

In order to perform the experiment, I filled the plastic dish with 10 mL of water. I placed the dish directly on the diaphragm of the speaker. I then connected the speaker to the function generator, so that when the function generator was set to a specific frequency, the speaker would play that sound, moving the diaphragm and creating waves in the water. I set the frequency to 10 Hz and took a slow-motion video of the patterns created in the water. I repeated this procedure with frequencies of 11Hz, 12Hz, 13Hz, 14Hz, 15Hz, 20Hz, 25Hz, 30Hz, and 35Hz. The independent variable was the frequency of the sound. And the dependent variable was the pattern created in the water. Controlled variables included the dish and speaker used, amount of water, and voltage of the function generator. I examined the results by viewing the videos of the experiment and observing the patterns created in each trial.

Results

At every frequency, the speaker created patterns in the water, with the distance between nodes getting noticeably smaller as the frequency increased. The only trial to create a very solid, repeating pattern was at a frequency of 14Hz, meaning the natural frequency of the water aligned with the frequency playing from the speaker.

14Hz-trimmed.mov

Slow motion video of results for the 14Hz trial.

Figure 6: The patterns created in the water when the frequency played was 14Hz. The design of the water alternated between the patterns shown in the two images.

Figure 7: The red and blue x’s represent the antinodes, where the system is oscillating at maximum or minimum amplitude. The area in between is the nodal lines, where the oscillation is zero and barely moving.

Calculations:

λ=vf

Speed of sound in water = 1481 m/s

Frequency = 14 Hz

λ=148114

λ=105.79m

Using the videos taken, I found the distance between nodes to be 4.53cm, thus the wavelength for 14Hz frequency in this model is 9.06cm.

There is uncertainty as to whether exactly 14Hz is a natural frequency for water because the plastic container was moving with the water when the speaker played the sound, so the results may have found the natural frequency for the plastic container or the combination of the container and water.

Discussion

Given the results, I found that there was clearly a lot more work required in predicting the patterns on the Chladni plate than just simply using the wavelength. The wavelength of the sound wave (105.8m) did not match up with the wavelength created in the water (9.06cm). Additionally, the many different variables of the experiment, including shape of the medium on which the water was placed, flexibility of the medium, shape and size of the speaker, etc., make it increasingly difficult to hypothesize the nodal lines. Predicting the patterns requires more complicated calculations than I had initially anticipated; however, information including Ernst Chladni’s equation for the relationship between the frequency and nodal numbers [f ∼ (m + 2n)^2] could become useful tools in the next steps towards hypothesizing the results in this experiment.

The movement of the water at different frequencies turned out to be very clear. In the future, some additional recording tools to get more accurate measurements between the nodes and antinodes as well as a device to prevent the medium from moving with the vibrations would be beneficial to increase the accuracy and clarity of the experiment.

Conclusion

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Sources

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