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).Omsin said: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.
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.pixel said: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?
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?sophiecentaur said: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, traveling 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.
Standing waves and superposition of traveling 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.Omsin said: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.
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.Omsin said: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?
When a string is plucked, it vibrates in a back-and-forth motion. This vibration causes the string to create sound waves, which travel through the air. These sound waves are perceived by our ears as sound. As the string continues to vibrate, it creates two pulses of sound waves, one traveling towards the left and one towards the right.
The reason for this is due to the physics of wave propagation. When a string is plucked, it creates a disturbance in the air molecules around it. This disturbance spreads out in all directions, creating a wave. As the wave travels through the air, it reflects off of objects and boundaries, creating a reflected wave. This reflected wave combines with the original wave, resulting in two pulses traveling in opposite directions.
The strength of the two pulses created by plucking a string depends on several factors, including the tension of the string, the length of the string, and the amplitude of the plucking force. The greater the tension and length of the string, and the larger the plucking force, the stronger the pulses will be. Additionally, the material and thickness of the string can also affect the strength of the pulses.
Yes, the two pulses created by plucking a string can have different amplitudes. This is because the amplitude of a wave is determined by the energy of the disturbance that creates it. In the case of plucking a string, the amplitude can be affected by the strength of the plucking force, as well as any damping or resistance in the string itself.
The two pulses created by plucking a string can interact with each other in various ways. When the pulses meet, they can either reinforce or cancel each other out, depending on their amplitudes and phases. This phenomenon is known as interference. In some cases, the interference can result in a standing wave, which is a pattern of stationary nodes and antinodes along the string.