Question about Natural Frequency and Resonance

[Thundagere]

So, I was reading a book on Nikola Tesla the other day, and it said that he said that he could theoretically split the Earth in two with resonance.
If I had a variable frequency oscillator, and I knew the natural frequency of an object, obviously I could create a standing wave. But, could I, as Tesla states, actually destroy it? Just clamp on the generator, and come back later to find it destroyde?
Secondly, what determines the amplitude of a standing wave set up by natural frequency. When you have a metal piece or a length of string it's the length that determines the wavelength, but what determines the amplitude?
Thanks for any help!

EDIT: Something else that's been bugging me...the Tacoma Narrows Bridge. The book said it was destroyed by winds hitting the natural frequency, which I presumed set up a standing wave. However, this seems...off, to me.. How could the winds hit and more importantly HOLD that frequency? Was it mere lack of structural integrity that destroyed this bridge,or was it the standing wave?

 

[Drakkith]

The bridge was actually destroyed due to Aeroelastic Flutter: http://en.wikipedia.org/wiki/Aeroelasticity#Flutter
http://en.wikipedia.org/wiki/Tacoma_Narrows_Bridge_(1940)#Cause_of_the_collapse

 

[Thundagere]

So the winds did cause it to hit the natural frequency and be destroyed? But how was it that the winds maintained that frequency for so long without changing?

 

[Drakkith]

So the winds did cause it to hit the natural frequency and be destroyed? But how was it that the winds maintained that frequency for so long without changing?

I'm not sure the wind needs to have a frequency.

 

[Thundagere]

Flutter is a self-feeding and potentially destructive vibration where aerodynamic forces on an object couple with a structure's natural mode of vibration to produce rapid periodic motion.

I took this to mean it matches the natural frequency, especially since "natural" is linked to natural frequency. Or am I missing something here?

 

[Redbelly98]

The winds were steady, not periodic. However, a steady wind blowing across a surface will produce wind vortices at a periodic rate, and it is this period that was in resonance with the Tacoma Narrows Bridge.

Think of a flag fluttering back and forth while a steady wind is blowing.

 

[Thundagere]

So essentially the ripples caused by the wind matched the frequency, which destroyed it...
Falling back to the original question, does that mean that, if I had a variable frequency oscillator, I could theoretically destroy anything, provided it was the same substance throughout?

 

[berkeman]

So, I was reading a book on Nikola Tesla the other day, and it said that he said that he could theoretically split the Earth in two with resonance.
If I had a variable frequency oscillator, and I knew the natural frequency of an object, obviously I could create a standing wave. But, could I, as Tesla states, actually destroy it? Just clamp on the generator, and come back later to find it destroyde?
Secondly, what determines the amplitude of a standing wave set up by natural frequency. When you have a metal piece or a length of string it's the length that determines the wavelength, but what determines the amplitude?
Thanks for any help!

EDIT: Something else that's been bugging me...the Tacoma Narrows Bridge. The book said it was destroyed by winds hitting the natural frequency, which I presumed set up a standing wave. However, this seems...off, to me.. How could the winds hit and more importantly HOLD that frequency? Was it mere lack of structural integrity that destroyed this bridge,or was it the standing wave?

So essentially the ripples caused by the wind matched the frequency, which destroyed it...
Falling back to the original question, does that mean that, if I had a variable frequency oscillator, I could theoretically destroy anything, provided it was the same substance throughout?

The amplitude of the oscillation at resonance depends on the "Q" or quality factor, and the amplitude of the driving source. The Q factor depends on how much damping there is in the structure. Thin crystal wine glasses can have a high Q factor, due to their thinness and hardness. You may have seen demonstrations of breaking wine glasses with and adjacent speaker, but you won't see the same demonstrations with a standard glass (unless the sound levels are crazy high).


EDIT -- here's a link for more reading:

http://en.wikipedia.org/wiki/Q_factor

.