فيزيائي 2009
31-01-2009, 15:42
Standing waves
Standing waves result when two sinusoidal wave trains of the same frequency are
moving in opposite directions in the same space and interfere with each other.[1] They occur when waves are reflected at a boundary, such as sound waves reflected from a wall or electromagnetic waves reflected from the end of a transmission line, and particularly when waves are confined in a resonator at resonance, bouncing back and forth between two boundaries, such as in an organ pipe or guitar string.
In a standing wave the nodes are a series of locations at equally spaced intervals where the wave amplitude (motion) is zero (see animation above). At these points the two waves add with opposite phase and cancel each other out. They occur at intervals of half a wavelength (λ/2). Midway between each pair of nodes are locations where the amplitude is maximum. These are called the antinodes. At these points the two waves add with the same phase and reinforce each other.
In cases where the two opposite wave trains are not the same amplitude, they do not cancel perfectly, so the amplitude of the standing wave at the nodes is not zero but merely a minimum. This occurs when the reflection at the boundary isn't perfect. This is indicated by a finite standing wave ratio (SWR), the ratio of the amplitude of the wave at the antinode to the amplitude at the node.
In resonance of a two dimensional surface or membrane, such as a drumhead or vibrating metal plate, the nodes become nodal lines, lines on the surface where the surface is motionless, dividing the surface into separate regions vibrating with opposite phase. These can be made visible by sprinkling sand on the surface, and the intricate patterns of lines resulting are called Chladni figures.
In transmission lines a voltage node is a current antinode, and a voltage antinode is a current node
Standing waves result when two sinusoidal wave trains of the same frequency are
moving in opposite directions in the same space and interfere with each other.[1] They occur when waves are reflected at a boundary, such as sound waves reflected from a wall or electromagnetic waves reflected from the end of a transmission line, and particularly when waves are confined in a resonator at resonance, bouncing back and forth between two boundaries, such as in an organ pipe or guitar string.
In a standing wave the nodes are a series of locations at equally spaced intervals where the wave amplitude (motion) is zero (see animation above). At these points the two waves add with opposite phase and cancel each other out. They occur at intervals of half a wavelength (λ/2). Midway between each pair of nodes are locations where the amplitude is maximum. These are called the antinodes. At these points the two waves add with the same phase and reinforce each other.
In cases where the two opposite wave trains are not the same amplitude, they do not cancel perfectly, so the amplitude of the standing wave at the nodes is not zero but merely a minimum. This occurs when the reflection at the boundary isn't perfect. This is indicated by a finite standing wave ratio (SWR), the ratio of the amplitude of the wave at the antinode to the amplitude at the node.
In resonance of a two dimensional surface or membrane, such as a drumhead or vibrating metal plate, the nodes become nodal lines, lines on the surface where the surface is motionless, dividing the surface into separate regions vibrating with opposite phase. These can be made visible by sprinkling sand on the surface, and the intricate patterns of lines resulting are called Chladni figures.
In transmission lines a voltage node is a current antinode, and a voltage antinode is a current node