Resonance in a wire ring

 Exploring wire ring resonance: after the wire snapped, we lost a few centimetres—but the same vibration patterns reappeared at new frequencies. Now predicting the new resonant points based on the lower original ones!

Wire Ring Resonance: Tuning Vibrations and Frequencies in a Circular Mystery

Resonance is one of those magical phenomena in physics—where the structure, shape, and material of an object interact with energy input to reveal natural, repeating patterns. In this experiment, we explored the elegant resonance of a wire ring mounted on a vibration generator. What happened next was both unexpected and illuminating.

The Setup

The wire, shaped into a loop, is fixed vertically on top of a vibration generator. As the frequency of the signal is increased, certain frequencies cause the wire to resonate. At these points, standing waves are formed around the ring, producing symmetrical, stable modes of oscillation. These are captured beautifully by the eye as blurred lobes, as seen in the image above—an example of one such resonant mode.

Each resonant mode corresponds to a harmonic frequency, dependent on:

• The length of the wire,

• The tension,

• The mass per unit length,

• And importantly, the boundary conditions (in this case, a continuous circular loop fixed at one point).

Disaster and Discovery

During one run of the experiment, the wire snapped.

While this might have seemed a setback, it actually provided a unique opportunity. We lost a few centimetres of the original length, which changed the natural resonant frequencies. But when we swept through the frequencies again, the same patterns appeared—albeit at slightly higher frequencies.

This confirmed an important principle: shorter wires resonate at higher frequencies. By observing the frequencies of the original wire and comparing them with those of the shortened wire, we were able to:

• Confirm the proportional relationship between frequency and wire length.

• Predict where new resonance points would appear, using harmonics of the base frequency.

Mathematical Insight

For a circular loop with fixed tension and uniform density, the resonance frequencies approximately follow:

$$f_n \propto \frac{n}{L}$$

Where:

• $f_n$ is the nth resonant frequency,

• $n$ is the mode number (number of nodes/antinodes around the ring),

• $L$ is the circumference of the loop.

After the wire snapped, $L$ decreased, causing an increase in all the $f_n$ values.

What You See in the Image

In the image, the wire exhibits a stable mode with several visible lobes (antinodes) around the ring. This is a higher harmonic, as evidenced by the multiple peaks around the loop. The symmetry suggests clean resonance, with very little damping—a hallmark of a well-tuned experimental setup.

Educational Value

This experiment beautifully illustrates:

• Harmonic motion,

• The impact of boundary conditions on resonance,

• How physical changes to a system (like shortening a wire) affect its natural frequencies,

• And the real-world applicability of wave physics equations.

It also makes for an excellent classroom demonstration:

• Easy to set up with a function generator and a signal amplifier,

• Visually impressive,

• And full of opportunities for both qualitative and quantitative analysis.

Next Steps

We're now working on:

• Mapping the harmonic series of the shortened wire and comparing it with the original,

• Modelling the loop using string wave equations adapted for a circular geometry,

• Using high-speed video to capture transitions between modes.

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Conclusion

Sometimes a snapped wire is not the end of an experiment—but the beginning of a deeper investigation. Wire ring resonance isn't just visually stunning; it's a fantastic demonstration of how physics helps us predict and understand the world through patterns, frequencies, and feedback.

Understanding Wire Ring Resonance — Questions for Curious Minds

🧠 Observation & Conceptual Questions

1. What do you notice about the shape of the wire in the image? What do the blurred sections represent?

2. Why do you think certain frequencies cause the wire ring to form symmetrical shapes while others don’t?

3. What does the term resonance mean in physics, and where have you seen it before (e.g., swings, music, bridges)?

4. Why do you think the resonant frequency increased when the wire became shorter?

5. How does this experiment show the relationship between length and pitch (like on a guitar or violin string)?

⚙️ Scientific Reasoning

6. If the original wire ring resonated at 60 Hz, and then a few centimetres broke off, would the new resonant frequency be higher or lower? Why?

7. The wire ring resonates in symmetrical patterns. What factors do you think affect how many ‘lobes’ appear?

8. Could this experiment be used to measure the tension in the wire? How might you go about doing that?

9. Would this experiment work the same way in space (zero gravity)? What forces are acting on the wire here?

10. How is this experiment similar to the behaviour of sound in a circular drum or a wine glass?

🧪 Creative & Practical Challenges

11. Design your own version of this experiment using string or elastic bands. What do you need to consider to get a clear resonance pattern?

12. If you were to double the mass of the wire, how might the resonance frequencies change? Try to predict and then explain.

13. How could you visualise this effect more clearly? What tools (e.g. high-speed camera, strobe light, motion tracker) might help?

14. Could you use this setup to make music? How would you ‘tune’ the wire?

15. Where else in engineering or nature do we see resonance being helpful—or dangerous? Can you give examples?

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