Dear Physicists, please I would like to know if there is a relation between the intensity of a signal acoustic wave and the ability of that wave signal to shatter a body. For instance, if a tuning fork is emitting an acoustic wave into body X (such as a glass cup) at a resonant frequency of body X (for instance the fundamental frequency) is there a threshold intensity (e.g. wave amplitude, wave power) of the wave emitted by the tuning fork which needs to be exceeded before body X will shatter? It seems well known that the shattering effect will occur at specific frequencies (the fundamental frequency or its harmonics) however, does the wave amplitude, power or other material properties of the body play a part? If yes, please what relation or formula governs these? Answers appreciated. Thanks
For a rigid or inelastic body to disrupt the applied force F must exceed the breaking strain. At resonance (Fr = 1/2pi Root(Cm M) Hz where Cm is the compliance, the inverse (= 1/K), of the spring deflection constant K. Now K is the deflection per unit force of the material and is related to Hook’s force/ extension constant for the material which defines the applied stress. This is implicit in the elastic modulus E (= stress/strain or Fl/delta la where ‘delta la’ is the length extension, ‘a’ cross sectional area and ‘F’ the force. If ‘K’ (thus Cm) describes the deflection per unit force for the material it is prescribed by the length and area subject to the force actually being used.. If now K = El/a then from the above K = Fl/delta a and the disruption force F = Kl delta a.
The force at resonance must exceed Kl delta a which must exceed E for disruption to take place. The acoustic power and its frequency must overcome E for the conditions of the material, i.e its temperature, level of intrinsic atomic faults, stress uniformity, etc. etc. Because of this it is very difficult to predict system disruption from first principles. However, experimentally a specific material can be modelled in terms of its behaviour and response to an acoustic force, allowing predictive equations to be formulated.
The above is a very simplified analysis and is not categorical.
Hi Barrie,
Thanks for this. Sorry for the late reply. Your post made me realize I have to study wave mechanics all afresh. I did do some vibration engineering in my undergraduate days before switching to business. Thanks a bunch and if I need further guidance, do I have permission to contact you?
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