# Where does resonance fundamentally come from?

Gold Member

## Main Question or Discussion Point

I know it has something to do with the natural vibrational states of atomic bonds (but does it also come from other sources?). But where do those natural vibrational states come from? Why do they tend to arise? And what exactly is the physical process through which resonance amplifies oscillation? Where does the energy come from?

And is this type of resonance fundamentally similar to say, orbital resonance?

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russ_watters
Mentor
The natural frequency of an object is based on the elastic modulus, which comes from the strength and type of bonds holding together the molecules. The natural frequency is the frequency at which an object will oscillate when struck.

Resonance occurs when an oscillating force is applied at the natural frequency, which pushes in the direction of motion, driving the oscillation, and increasing the amplitude of the modulation.

And yes, resonance is resonance. Orbital resonance occurs when the force of gravity between two objects is applied at some regular interval that results in an oscillation.

DaveC426913
Gold Member
The natural frequency of an object is based on the elastic modulus, which comes from the strength and type of bonds holding together the molecules. The natural frequency is the frequency at which an object will oscillate when struck.

Resonance occurs when an oscillating force is applied at the natural frequency, which pushes in the direction of motion, driving the oscillation, and increasing the amplitude of the modulation.

And yes, resonance is resonance. Orbital resonance occurs when the force of gravity between two objects is applied at some regular interval that results in an oscillation.
Does it not also have something to do with the macro size of the object? i.e. a 10cm steel ball will resonate at a different freq than a 20 cm steel ball because of internal reflections?

Andy Resnick
"resonance", defined in terms of how it is measured, occurs in the absense of dissipation. So, in order to talk about where resonance "comes from", one must understand dissipation.

Dissipative processes can be decribed many ways, but in essence dissipation acts to decohere input energy. For example, the coherent field within a microwave resonantly excites water rmolecules, and collisions of the water molecules with other molecules dissipates the coherent EM energy into thermal energy. Exciting a tuning fork with an impulse excites many vibrational modes, most of whom are nonresonant and quickly dissipate their energy- I don't know if the energy can flow into the resonant mode, but strain waves are nonlinear so it may be possible.

What physical processes are involved- there are many types of resonant excitation; mechanical is the obvious one, but one also speak of resonant EM cavities or molecular excitations as well. There are many possible mechanisms involved.

russ_watters
Mentor
Does it not also have something to do with the macro size of the object? i.e. a 10cm steel ball will resonate at a different freq than a 20 cm steel ball because of internal reflections?
Yes - my explanation was perhaps a bit thin. The equation for natural frequency is simply w=k/m and the elastic modulus is a spring constant... in terms of unit length/area.
We may say that Young's modulus is the Hooke's-law spring constant for the spring made from a specifically cut section of the solid material, cut to length 1 and cross-sectional area 1. The shape of the cross-sectional area does not matter.
http://ccrma.stanford.edu/~jos/pasp/Young_s_Modulus_Spring_Constant.html

But for most shapes, then, Young's modulus needs some sort of geometry conversion. The specific conversion depends on the axis of oscillation (ie, an I beam will have 3 basic natural frequencies, one for each axis).

I like Andy's treatment of the subject.

In term's of vibrational modes, are these vibrations felt by every atom in the substance? What kinds of vibrations are we talking about with respect to each atom, torsional?