Ghanta and Vajra – Tibetan prayer bell physics

Presenter: Andy Jackson, Harrisonburg City Schools, ajackson@harrisonburg.k12.va.us.   

Va. SOL:

PH.1          The student will plan and conduct investigations using experimental design and product design processes. Key concepts include

a)     the components of a system are defined;
b)     instruments are selected and used to extend observations and measurements;
c)     information is recorded and presented in an organized format;
d)     the limitations of the experimental apparatus and design are recognized;
e)     the limitations of measured quantities are recognized through the appropriate use of significant figures or error ranges;
f)     models and simulations are used to visualize and explain phenomena, to make predictions from hypotheses, and to interpret data; and
g)     appropriate technology, including computers, graphing calculators, and probeware, is used for gathering and analyzing data and communicating results.

PH.2          The student will investigate and understand how to analyze and interpret data. Key concepts include

a)     a description of a physical problem is translated into a mathematical statement in order to find a solution;
b)     relationships between physical quantities are determined using the shape of a curve passing through experimentally obtained data;

PH.8          The student will investigate and understand wave phenomena. Key concepts include

a)     wave characteristics;
b)     fundamental wave processes; and
c)     light and sound in terms of wave models.

• illustrate period, wavelength, and amplitude on a graphic representation of a wave.
• solve problems involving frequency, period, wavelength, and velocity.
• distinguish between superimposed waves that are in-phase and those that are out-of-phase.
• graphically illustrate constructive and destructive interference

Topic/Concept

Students will investigate the sound produced by a bell sounded three different ways, and interpret graphical and mathematical representations of the sound data with regard to the way their hearing discerns the differences.

Materials

• Tibetan prayer bell Click here to do an eBay search for "Tibetan Prayer bell."
• Vernier microphone and LabPro, or LabQuest

Here is a video of several sized Tibetan prayer bells being played.

Here is the link to the YouTube video: http://youtu.be/dfM7i12Hdgg

Alternative Materials List

• Fluted Champaign glass 1/2 filled with water
• Spoon (acts as a clapper.)
• Use a wet finger as the wooden striker.

Safety Considerations

Do not strike the bell while holding close to someone’s ear. If you are using the glasses, do not hit them too hard so as to break them.

Presentation

This bell can be sounded by clapper, wooden striker, and resonance. The student uses the microphone and vernier software to record and analyze the three different sounds.

How the physics is demonstrated

This gives the student a chance to examine frequency, period, resonance, beats, wave superposition, and explore the ability of the human ear to discern slight differences in sound.

Construction  and Tips Regarding the Demonstration

None

Sources & References

None

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This Tibetan prayer bell can be sounded three different ways. It can be swung slightly so the clapper strikes the bell, it can be struck with the wooden striker, or it can be sounded through resonance by gliding the wooden striker around the rim of the bell (like your finger along the rim of a wine glass). In ceremonies using these items the bell (called Ghanta) represents the feminine and wisdom, and the double scepter (called Vajra) represents masculine and skillful methods. It seems an interesting parallel to bring them together in science – wisdom and skillful methods; essential understanding and scientific skills.

Ring the bell all three ways with essentially equal volume of sound.  Listen carefully and describe the differences in sounds they produce. Do not  pay attention to the initial moment of ringing, but of the sound created and sustained after initiation of the sound.

Clapper

 

Wooden striker

 

Resonance

 

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Do you hear one sound? Variations in sound?

 

Use a microphone hooked up to the LabQuest2 to record the sound. Put the settings to record for 1.00 s at a rate of 10,000 points per second.

Save each of the recorded sounds as a uniquely named file that makes sense so you know which file represents which way of ringing the bell.

Examine each of the traces. Zoom in to see the fine details. What are you are seeing that connects to the sounds or the difference in sounds you noticed earlier? 

Zoom in to the “smoothest” of the sounds until you can see several wavelengths of the sound being made. Use the curve fit and choose “sine” to fit a function to the data.

Take the value of B and divide it by 2π. This answer is the frequency of the wave. It is the frequency of the sound you were hearing. What is the frequency?

 

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• Zoom back out an look at the larger pattern
• Use the examine tool to find the time that adjacent peaks or troughs occur in this bigger pattern.
• Do the math to find the period of this pattern.
• Determine the frequency of the larger pattern.

Apply a Fast Fourier Transform to the data.  A Fast Fourier Transform (FFT) takes a complicated wave and breaks it into multiple simple sine waves that when added together make up the single complex pattern. The image will look something like this once you have zoomed into the dominant peak to examine things more closely.  Use the examine tool to find the frequency of the two dominant frequencies (or frequency clusters)

1. What are the two dominant frequencies?
2. How do they compare to the sine curve fit you performed earlier?
3. What is the difference between the two  dominant frequencies in the FFT?
4. How does this answer compare to the frequency of the big picture pattern?
5. Examine the three different methods of ringing the bell using the tools described. See if you can analyze and explain any differences you were hearing in the three different methods.