Help with understanding resonance

[Anonymstudent]

Hi there,

I am trying to understand resonance, but i haven't wholly grasped the concept.
As far as my knowledge goes, if one evokes a wave upon an object, at the same fundamental frequency as the object, then a standing wave occurs and the object "resonates"

the obvious case is the singer and glass smashing. Singer sings at natural frequency of glass, the wave interferes with the natural vibration and the amplitude goes haywire and breaks the glass. I am assuming that the natural vibration can be neglected, because if it was larger then we would be able to hear a sound coming from it. Thus, won't the glass break no matter the frequency of the singer's waves with a high enough amplitude?
And on the same reasoning, the glass could be smashed if the singer sings at any frequency?

thanks in advance

 

[Feldoh]

The idea is that if we drive something at it's natural frequency the oscillations will become very large.

If we look at what is happening actually I think it might help. In the case of the singer the singer is creating a pressure wave which makes the molecules in the air vibrate. This pressure wave causes a force on the glass.

So now that we know that as the singer sings he/she is inadvertently exerting a force on the glass.

Obviously now, if the singer sings loud enough the force will be strong enough to break the glass. Physically it *could* happen but it's pretty much impossible that anyone could sing loud enough.

Or if the singer can hold the right frequency at a relatively loud volume (but still a practical loudness) we can drive the glass into oscillations at resonance, if these vibrations are strong enough the glass will shatter, but at a much lower loudness than in the previous example.

We can think about the energy and the power that we are transferring to the glass in each of these scenarios as well. The louder the singing the larger the pressure wave will be (however it will still propagate with the same frequency regardless of loudness). In the first case we need a large amount of energy in order to shatter the glass and in the second case we needed a relatively smaller amount of energy. This has to do with how well the glass can absorb the energy.

If you look at it what you will find is that energy is more efficiently transmitted to an object if the frequency of the energy is near the resonant frequency of the object. This relates to something that physicists call the "Q factor" or quality factor.

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So to answer your question, yes, the glass will shatter at a high enough amplitude regardless of frequency. The caveat is that at frequencies far from the resonant frequency the energy we transfer to the glass is a lot less efficient than if we were to transmit energy with a frequency near the resonant frequency. Does that answer your question?

 

[Anonymstudent]

Ah, that helps, thanks a lot Feldoh!