# Standing waves and reflection

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)

sophiecentaur
Gold Member
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).

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.

sophiecentaur