Coursework Stress Fracture

Shattering a Wine Glass with Sound

Anthony Scodary
December 9, 2007

(Submitted as coursework for Physics 210, Stanford University, Autumn 2007)

Fig. 1: A vibrating wine glass. The fundamental mode distorts the circular rim into an ellipse.

Introduction

The image of an opera singer breaking glass with her booming voice is not a new one. From cartoons to Ella Fitzgerald in the classic 1970's Memorex commercial, the association between loud, piercing sounds and shattering glass is very familiar. It should come as no surprise this phenomenon has been tested and retested in a wide variety of acoustical situations, and it turns out that it is indeed very possible to shatter a wine glass with nothing but ordinary sound waves.

The typical experimenter will begin by tapping a wine glass to excite the fundamental frequency associated with natural oscillations (the fundamental mode of vibration entails the circular rim of the glass periodically distorting into an ellipse). Using a spectrum analyzer, strobe light, musician with perfect pitch, or whatever methods desired, the experiment discovers the fundamental frequency. This frequency is then usually mimed over a loud speaker (or by an opera singer perhaps). At resonance, the wine glass distorts and strains until the brittle vessel fractures violently. This phenomenon is a demonstration of both the fragility of glass and the often surprising power of resonance.

The Strength of Glass

Unlike materials such as quartz or iron, the molecules in glass are arranged in an amorphous structure rather than a crystal. The lack of a crystal lattice structure makes glass very brittle, and it shatters via a conchoidal fracture that does not exhibit planes of separation. Most ordinary glass used in windows and jars is soda-lime glass, while many drinking glasses are made from borosilicate glass instead to protect them from the thermal strain of hot beverages.

In fracture mechanics, the typical measure of fracture resistance is fracture toughness, which describes the ability of a material containing a crack to resist fracture. For glass, the value of the fracture toughness is KIc = 0.7 MPa-m1/2, compared to about 50 MPa-m1/2 for steel. The fracture toughness is related to the stress σ and crack length a by

Most glass will contain microscopic cracks that serve as the seed crack from the fracture. For a thin sheet of material in a wine glass, the weak material properties of glass substantially ease the ability of sound pressure waves to meet the energy threshold of a fracture.

Fig. 2: The amorphous structure of glass has limit means for energy absorption and strength.

Acoustic Resonance

The destructive power of resonance and forced oscillations is probably most famously demonstrated by the collapse of the Tacoma Narrows Bridge in the presence of strong winds. Small inputs of energy at the right frequency can often compound into violent structural failures.

The vibration of the fundamental mode of the wine glass can be crudely modeled as an damped harmonic oscillator with a resonant frequency equal to the fundamental mode's frequency. The coupling of the wine glass to the pressure waves of sound is analogous to the coupling of sympathetic vibrations between two tuning forks with the same frequency. Striking one tuning fork will allow some of the acoustic energy to excite the other tuning fork via the resonant coupling. The sound source in this case, be it a large speaker or simply a human voice, acts to drive the wine glass.

The intensity of the vibrational response is dependent on the line width caused by dampening. With little or no dampening, the intensity I(ω) is a delta function at the resonant frequency. I(ω) is described by the frequency-domain Lorentzian equation:

Where gamma is the linewidth and ω is the resonant frequency. Although, dampening caused by impurities in the glass and its amorphous structure causes a widening of the frequency response. Lead crystal tends to have significantly less dampening, which is demonstrated by the long, pure ring when a crystal glass is struck. Low-quality glass will often ring with a brief, dull tone. It turns out that in most demonstrations of this effect, a typical function generator (or singer) precision of plus or minus 1/2 Hz is sufficient to match the resonant frequency.

Acoustic Energy and Fracture

Due to the finite dampening in a wine glass, it is necessary to provide sufficient energy to overcome the dampening to the point of catastrophic stress. In most demonstrations, the necessary loudness of the exciting sound is very, very loud at approximately 135-140dB. This corresponds to a pressure perturbation of roughly 200Pa. This pressure level is approximately the loudness of a rifle being fired from a distance of 1m, and is normally beyond the threshold of pain for the human ear. For a single, sustained frequency, such a noise would be very painful and piercing to most listeners anywhere near the experiment.

Using Amplified Sound and Human Voice

The most common question about the phenomenon of breaking a wine glass with sound is whether the feat can be performed with unamplified human voice. Normal conversation takes place at around 50dB, so for a human to sing a pure pitch as loud as 140dB is possible but very challenging. While the phenomenon has been demonstrated with unamplified human voice, it is a very challenging feat, that likely requires very pure glass and a booming singer. Using amplified sound over large speakers is very doable with good equipment, but generally the energy levels involved in shattering glass with sound are very high and both the sound waves and the shards of glass can be very harmful to the experimenter if proper precautions are not taken.

© 2007 Anthony Scodary. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.

References

[1] K. Billah and R. Scanlan, "Resonance, Tacoma Narrows Bridge Failure and Undergraduate Physics Textbooks," Am. J. Phys. 59, 118 (1991).

[2] T. L. Anderson, "Fracture Mechanics: Fundamentals and Applications" (CRC Press, 1995).

[3] T.D. Rossing, "Acoustics of the Glass Harmonica," J. Acoust Soc. Am. 95, 1106 (1994).

[4] A. P. French, "In Vino Veritas: A Study of Wineglass Acoustics," Am. J. Phys. 51, 688 (1983).

[5] R. E. Apfel, "'Whispering' Waves in a Wineglass," Am. J. Phys. 53, 1070 (1985).

Stress concentrations, Mohr’s Circle for Plane Strain, and measuring strains

In this section, we will learn about stress concentrations, and discuss plane strain, develop Mohr’s Circle for Plane Strain, and explore methods of measuring strain.

Graded: Quiz on Stress concentrations, Mohr’s Circle for Plane Strain, and measuring strains

  1. Video: Module 27: Stress Concentration Factors/Saint-Venant’s Principle
  2. Reading: Download Pdf Format Module 27: Stress Concentration Factors/Saint-Venant’s Principle
  3. Video: Module 28: Determine Maximum Stress at Discontinuities using Stress Concentration Factors
  4. Reading: Download Pdf Format Module 28: Determine Maximum Stress at Discontinuities using Stress Concentration Factors
  5. Video: Module 29: Two-Dimensional (2D) or Plane Strain
  6. Reading: Download Pdf Format Module 29: Two-Dimensional (2D) or Plane Strain
  7. Video: Module 30: Transformation Equations for Plane Strain
  8. Reading: Download Pdf Format Module 30: Transformation Equations for Plane Strain
  9. Video: Module 31: Transformation Equations for Plane Strain (cont.)
  10. Reading: Download Pdf Format Module 31: Transformation Equations for Plane Strain (cont.)
  11. Video: Module 32: Mohr’s Circle for Plane Strain
  12. Reading: Download Pdf Format Module 32: Mohr’s Circle for Plane Strain
  13. Video: Module 33: Determine Principal Strains, Principal Planes, and Maximum Shear Strain using Mohr’s Circle
  14. Reading: Download Pdf Format Module 33: Determine Principal Strains, Principal Planes, and Maximum Shear Strain using Mohr’s Circle
  15. Video: Module 34: Strains on any given plane using Mohr’s Circle
  16. Reading: Download Pdf Format Module 34: Strains on any given plane using Mohr’s Circle
  17. Video: Module 35: Find Strains using Experimental Analysis Techniques
  18. Reading: Download Pdf Format Module 35: Find Strains using Experimental Analysis Techniques
  19. Video: Module 36: Find In-Plane Strains using Strain Gage Measurements
  20. Reading: Download Pdf Format Module 36: Find In-Plane Strains using Strain Gage Measurements
  21. Video: Module 37: Find Principal Strains, Maximum Shear Strain, and Principal
  22. Reading: Download Pdf Format Module 37: Find Principal Strains, Maximum Shear Strain, and Principal
  23. Reading: Solution to Quiz Week Four

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