Conservation of energy in standing wave

AI Thread Summary
A standing wave on a string, created by transverse oscillations at the third harmonic, does not violate the conservation of energy despite the string's greater amplitude compared to the oscillator. The principle of conservation of energy is upheld because the energy from the oscillator is transferred to the string, resulting in the superposition of wave displacements. This leads to a larger amplitude in the standing wave without creating energy from nothing. Additional resources on resonance were provided for further understanding. The explanation given is considered valid and concise.
Saxby
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Homework Statement


A standing wave is produced by small transverse oscillations of one end of a taught string stretched between an oscillator and a fixed point. The frequency of oscillation is adjusted to be resonant at the third harmonic.

The amplitude of the string's viabration is very much greater than that of the oscillator.
(i) Does this violate the principle of conservation of energy?
(ii) Explain why

The Attempt at a Solution


I do not believe this would violate the conservation of energy.

I think that if a standing wave is formed the addition (via superposition) of the displacements of points on the new and reflected waves should be more than that of the oscillator.

Does that sound like a valid explanation?
 
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Saxby said:

Homework Statement


A standing wave is produced by small transverse oscillations of one end of a taught string stretched between an oscillator and a fixed point. The frequency of oscillation is adjusted to be resonant at the third harmonic.

The amplitude of the string's viabration is very much greater than that of the oscillator.
(i) Does this violate the principle of conservation of energy?
(ii) Explain why

The Attempt at a Solution


I do not believe this would violate the conservation of energy.

I think that if a standing wave is formed the addition (via superposition) of the displacements of points on the new and reflected waves should be more than that of the oscillator.

Does that sound like a valid explanation?
'Sounds like a fair explanation to me. :approve: (Edit: As a matter of fact, that's about the most concise explanation I can think of. I'd give you full credit.)

But just for good measure, here are a couple of links on resonance, for further research.
http://hyperphysics.phy-astr.gsu.edu/hbase/sound/reson.html
http://en.wikipedia.org/wiki/Resonance
 
Last edited:
I also asked my lecturer and he said it sounded ok, thanks for your reply :)
 
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