I Why plucking of string creates two pulses?

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1. May 7, 2017

Omsin

When we pluck a string and a triangle is formed. Why does this triangle form into two opposite moving pulses? If we have reflective edges the two pulses will reflect, invert and superposition into the same triangle wave on the under side of the string. Let's say we have no dampening.

I think it has something to do with standing waves, but I am not really certain.

2. May 7, 2017

pixel

Are you asking why there are two pulses instead of just one? Aren't the initial conditions the same on both sides of the triangle? What would there be to favor one side vs. the other?

3. May 7, 2017

sophiecentaur

When the string is released from its triangular shape (plucked nearer one end than the other - not in the middle), the spectrum of waves on the string will correspond to the normal modes of oscillation (standing waves that will sustain themselves) on the string . The spectrum of those modes (amplitude and phase) is given by the Discrete Fourier transform of the starting shape. For an ideal string, these modes correspond to odd harmonics of the fundamental mode of oscillation of the string (one antinode in the middle).
You can look upon these modes as pairs of waves, travelling in each direction, all of which will add together to produce the original triangle and another triangle shape, reflected in the other end and upside down.
If you pluck / displace the string fast enough, the shape doesn't have to be a triangle. Many of the diagrams that you can find will be a single short pulse that's launched in just one direction but that's actually hard to achieve because a wave will go in both directions from the start position.
See this link for an animation plus a number of useful ideas.

4. May 7, 2017

Omsin

Yes, same initial conditions. But is it something more behind it than a symmetry argument? That is why I was asking about standing waves and superposition.

5. May 7, 2017

Omsin

Thank you for your reply. I read the article,but had problem understanding "the normal mode of oscillations". But how is it then possible to create a single pulse traveling along the string?

6. May 7, 2017

sophiecentaur

Standing waves and superposition of travelling waves are just alternative ways of analysing the same phenomenon. You can have impressed waves of any frequency moving along a string but they will only arrive in the right places and at the right times to form a standing wave if they correspond to the normal modes.
Did you look at that link with its animation. The animation was produced by calculation and is not just an "artist's impression".
Waves can also be introduced onto a string by a vibrator of some kind. (forced oscillation) This way, a wave of any frequency can be launched but it will not build up unless it is one of the normal modes of the string.

7. May 7, 2017

sophiecentaur

You can launch a single pulse from one end and then quickly clamp that end again. The pulse will be reflected from the other end and then each end. Because of the time taken for the transit, that limits the frequencies involved and you still have your normal modes involved.