Thursday, August 18, 2011
Standing waves Waves combine by superposition to make unique sounds, which comes about from the mathematical principle of superposition: the total amplitude for a sum of waves is the sum of the amplitudes of the individual waves. A wave of a single frequency will graph as a very regular and well-behaved sine wave, but the graph of any random sound is likely to have stranger variations in amplitude and period. At the points where the amplitudes of the waves are all positive or all negative, the waves are in constructive interference because the absolute value of the total amplitude is maximum. At points where the signs of the amplitudes are different, the waves “cancel each other out” and are in a state of destructive interference. One interesting result is the standing wave pattern, named for the way that its nodes never seem to move. On a graph of a wave’s amplitude, a node is any place that the amplitude touches or crosses the horizontal axis because it is a point of zero-amplitude oscillation. The waves making up a standing wave all destructively interfere at the standing wave’s nodes at all times t, meanwhile letting the other parts of the graph oscillate in amplitude. This is what gives the wave the impression of standing or waving in place. (It is easy to fashion your own standing waves at home. If you tie a jump rope to a tree and start swinging it, you have created a standing wave where the nodes are at the tree and your hand. If you get really good and your rope is very long, you can swing it so that one or more nodes appear in the middle, and many people can jump rope together.) Especially with sound, standing waves are significant because they represent tones that resonate in the medium, such as harmonics and overtones. If you are in a resonant room, you might find that certain pitches resound through the room while others die off quickly. The pitch that resonates is associated with a sound wave that can set up a standing wave in that particular room (by reflecting off the walls and interfering with itself). On a string instrument, one can create different standing waves by touching a fingertip to a place on the string to manually induce a node. The intricate connections between resonance and standing waves are the foundation for musical harmony.

Standing waves

Waves combine by superposition to make unique sounds, which comes about from the mathematical principle of superposition: the total amplitude for a sum of waves is the sum of the amplitudes of the individual waves. A wave of a single frequency will graph as a very regular and well-behaved sine wave, but the graph of any random sound is likely to have stranger variations in amplitude and period. At the points where the amplitudes of the waves are all positive or all negative, the waves are in constructive interference because the absolute value of the total amplitude is maximum. At points where the signs of the amplitudes are different, the waves “cancel each other out” and are in a state of destructive interference.

One interesting result is the standing wave pattern, named for the way that its nodes never seem to move. On a graph of a wave’s amplitude, a node is any place that the amplitude touches or crosses the horizontal axis because it is a point of zero-amplitude oscillation. The waves making up a standing wave all destructively interfere at the standing wave’s nodes at all times t, meanwhile letting the other parts of the graph oscillate in amplitude. This is what gives the wave the impression of standing or waving in place.

(It is easy to fashion your own standing waves at home. If you tie a jump rope to a tree and start swinging it, you have created a standing wave where the nodes are at the tree and your hand. If you get really good and your rope is very long, you can swing it so that one or more nodes appear in the middle, and many people can jump rope together.)

Especially with sound, standing waves are significant because they represent tones that resonate in the medium, such as harmonics and overtones. If you are in a resonant room, you might find that certain pitches resound through the room while others die off quickly. The pitch that resonates is associated with a sound wave that can set up a standing wave in that particular room (by reflecting off the walls and interfering with itself). On a string instrument, one can create different standing waves by touching a fingertip to a place on the string to manually induce a node.

The intricate connections between resonance and standing waves are the foundation for musical harmony.

Posted at 8:06 PM 27 notes Tags: animation constructive interference destructive interference do this at home harmonics harmony jump rope mechanical wave music musical sound overtones physics resonance science sound waves standing wave superposition waves waves on a string wikipedia sayitwithscience

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