Standing waves and reflection

  • Thread starter gracy
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  • #26
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You should qualify that statement. Frequency times wavelength is wave speed, so for a non dispersive medium (only) the wavelength will be inversely proportional to frequency.

Also, something that has not been brought up yet is the fact at a real standing wave (when the string is vibrating at resonance) is best thought of as many many waves (not just 'a wave' going left and 'a wave' going right) -it is the result of all the sections of the original launched wave, going up and back, endlessly because the returning wave is also reflected by the source end. This is not often mentioned in popular 'explanations'. The fact is that all standing waves will dissipate some energy (Friction / radiated sound / resistance / radiated EM waves etc). Without some steady loss of energy, the wave will just grow and grow, building up each time the initial wave does a lap and extra energy is added. The final amplitude reached as a standing wave builds up is when the rate of energy put in is equal to the rate of energy loss. When the source end has 'just the right' resistive impedance, the returning energy will be dissipated so the peaks of the standing wave will be least, Then you will actually, no longer have actual resonance and there will be a small standing wave for all frequencies (because of only one far end reflection). Most demos of standing waves will involve a loosely coupled input signal and it may take several hundreds of cycles before the amplitude builds up to a maximum.
Videos of standing waves on strings will always tend to miss showing the string when it is horizontal because it is at its maximum speed at that time. Each section of the string performs Simple Harmonic Motion; with amplitude which depends on the position on the string. There is much less blurring at the maximum extremities of the motion so the camera catches that part most. (That's the same for all SHM depiction).
in standing wave there would be a instant when string is totally horizontal but not in normal waves(such as if the only wave is coming from right ,not superposing with any other wave)
 
  • #27
sophiecentaur
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in standing wave there would be a instant when string is totally horizontal but not in normal waves(such as if the only wave is coming from right ,not superposing with any other wave)
And so there is. Just because a demonstration doesn't appear to show it, doesn't mean it's not there. Consider just how long the 'straight line' position lasts. This is the same as when an oscillator goes through the equilibrium position (see my previous post).
 
  • #28
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This is the same as when an oscillator goes through the equilibrium position
But there would be no such instant when the complete string is horizontal in normal waves (i.e waves other than standing wave)of string .Because only points which are in same phase will be at equilibrium position at a given point of time,and two adjacent points can never be in same phase.So the string would never be totally horizontal.That's what i said in my previous post.
 
  • #29
sophiecentaur
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But there would be no such instant when the complete string is horizontal in normal waves (i.e waves other than standing wave)of string .Because only points which are in same phase will be at equilibrium position at a given point of time,and two adjacent points can never be in same phase.So the string would never be totally horizontal.That's what i said in my previous post.
Of course not. The stationary parts are at the maxima and minima, as the string changes direction and that is where the string would he horizontal for an instant. You are just pointing our the essential difference in appearances of the two forms of wave. OK, now move on.
I am not sure what you are trying to get out of this thread. The theory is clear enough and you can find it presented at many different levels with a Google search. Standing and progressive waves are different beasts. The standing wave occurs when there are two or more waves of the same frequency which interfere in a way such that the string (or whatever) oscillates in a particular way. I fear that it is unlikely that anyone can provide you with an 'explanation' that will satisfy you about this unless you sit down on your own and try to come to terms with what you have been told (or what you have read) so far.
I am still not clear what you understand about Oscillations because you need to have this sorted before waves will make any sense. I suspect that you are trying to fast track into this without the basics and you are unlikely to succeed that way.
 

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