Standing Waves Standing Waves standing wave – also known as a stationary wave – is a wave that remains in a constant position. This phenomenon can occur because the medium is moving in the opposite direction to the wave, or it can arise in a stationary medium as a result of interference between two waves traveling in opposite directions. In the second case, for waves of equal amplitude traveling in opposing directions, there is on average no net propagation of energy. Opposing waves :- As an example of the second type, a standing wave in a transmission line is a wave in which the distribution of current, voltage, or field strength is formed by the superposition of two waves of the same frequency propagating in opposite directions. The effect is a series of nodes (zero displacement) and anti-nodes (maximum displacement) at fixed points along the transmission line. Such a standing wave may be formed when a wave is transmitted into one end of a transmission line and is reflected from the other end by an impedance mismatch, i.e., discontinuity, such as an open circuit or a short. The failure of the line to transfer power at the standing wave frequency will usually result in attenuation distortion.
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In practice, losses in the transmission line and other components mean that a perfect reflection and a pure standing wave are never achieved. The result is a partial standing wave, which is a superposition of a standing wave and a traveling wave. The degree to which the wave resembles either a pure standing wave or a pure traveling wave is measured by the standing wave ratio (SWR). Another example is standing waves in the open ocean formed by waves with the same wave period moving in opposite directions. These may form near storm centres, or from reflection of a swell at the shore, and are the source of microbaroms and microseisms. Mathematical description :- In one dimension, two waves with the same frequency, wavelength and amplitude traveling in opposite directions will interfere and produce a standing wave or stationary wave. For example: a wave traveling to the right along a taut string and hitting the end will reflect back in the other direction along the string, and the two waves will superpose to produce a standing wave. The reflective wave has to have the same amplitude and frequency as the incoming wave. If the string is held at both ends, forcing zero movement at the ends, the ends become zeroes or nodes of the wave. The length of the string then becomes a measure of which waves the string will entertain: the longest wavelength is called the fundamental. Half a wavelength of the fundamental fits on the string. Shorter wavelengths also can be supported as long as multiples of half a wavelength fit on the string. The frequencies of these waves all are multiples of the fundamental, and are called harmonics or overtones. For example :- a guitar player can select an overtone by putting a finger on a string to force a node at the proper position between the ends of the string, suppressing all harmonics that do not share this node.
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Sound Waves :- For sound waves the existence of material medium is very necessary for the propagation of the waves. The propagation of waves taking place in solid, liquid and gases which makes us hear the sound is called Sound wave. Properties :1. Sound waves are longitudinal in nature. 2. Material medium is necessary for the propagation of the sound waves. 3. The Speed of sound in air at N.T. P is 332 m/s. 4. The Sound is audible only between 20 Hz to 20 KHz. Standing Waves :When a wave remains in a constant position it is called Standing wave. This is possible due to 2 reasons: 1. When the medium moves in a direction opposite to the direction of propagation of wave it is possible. 2. When the phenomenon of interference takes place between the two waves traveling in an opposite direction then it is possible. When two waves having equal frequency and amplitude overlap each other then we get a standing wave. This is possible due to the obstruction of the wave by some boundary and hence the reflection of it back in the same medium.
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