Dhristi JEE 2022-24

What is the Standing Wave?

The term standing wave is also called the stationary wave. The standing waves definition is similar to the stationary wave and carries a similar equation. The periodic disturbance in a medium caused by the interaction of two equal-frequency-and-intensity waves traveling in opposing directions. There is no net transfer of energy in a standing wave.

In other words, it means the combination of two different waves flowing in opposing directions, carrying the same amplitude and frequency. Interference causes the occurrence; when waves are overlaid, the energy is added together or erased out. To understand the standing waves definition, there is a rope with two endings; another wave traveling down through the rope will clash with the reflected wave. Standing waves are created when the nodes and antinodes stay in the same position over time at specified frequencies. The nodes and antinodes alternate with equal spacing for the frequencies of the standing wave.


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Positions along the medium that are motionless are characteristic of all standing waves. Nodes are the names given to these places. The meeting of a crest and a trough results in nodes. This results in a location where there is no displacement. Antinodes are another feature of standing waves. These are the points along the medium where the particles fluctuate with the greatest amplitude around their equilibrium location. Antinodes are formed when a crest meets another crest and a trough meets another trough. An alternating pattern of nodes and antinodes is always present in standing wave patterns.


How is the Standing Wave Formed?

One of the familiar doubts people have is about how is standing wave is formed. To get an idea, here is an example-

Consider a rope that is stretched in the room, about 4-meters long from end to end. If there is an upward displaced pulse connected at the rope’s left end, it will move rightward through the rope until reaching the right side of the fixed end. The single pulse will reflect and invert when it reaches the fixed terminus. The upward displaced pulse turns into a downward displaced pulse. Assume that a second upward displaced pulse is injected into the rope during the same time that the first crest's fixed end reflection occurs. A rightward moving, upward displaced pulse will meet up with a leftward moving, downward displaced pulse at the precise middle of the rope if this is done with perfect time. This standing wave example will give a clear idea of the Standing wave ratio formula, ratio, and equation derivation.


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Standing waves only form on a string when forces at the ends prevent the string from moving above or below the fixed end. Standing waves form in an acoustic chamber only when pressure prevents air from flowing into or out of the immovable walls. In a microwave cavity, standing waves form when charges and currents at the cavity's walls cause the electric field's normal component and the magnetic field's transverse component to adopt the right values.

To get the standing wave ratio formula, one needs to work on the VSWR (Voltage Standing Wave Ratio). The normal method of expressing voltage standing wave ratio formula is- a perfect match, i.e. a short or open circuit, is 1:1, while a total mismatch, i.e. a short or open circuit, is 1. According to the specification, VSWR equals maximum voltage on the line and is further divided with minimum voltage. The voltage variations are caused by the summation of the voltage components from the forward and reflected power sources. This also represents the standing wave equation.

The formula allows the VSWR in a feeder to be estimated in various ways depending on the given information. Depending on the measurements that can be taken, multiple parameters will be accessible at different times. The VSWR may be estimated using a variety of other relationships or formulae under a range of scenarios. This also gives a clear picture of the standing wave equation derivation.


Production of Stationary Waves

One example to explain the production of standing waves is if we pluck one string from the guitar, there is a vibration within the object, which is called the mechanical waves. This vibrating instrument helps in producing sound through vibrations and the air and reaches to ears.

Common Mistakes

The string's length determines the length of the standing wave. Endpoints will always be nodes, and the wavelength of the first harmonic will always be double the length of the string, regardless of how long the string is.


Conclusion

The repetitive interference of two waves of same frequency traveling in opposing directions through the same medium results in standing wave patterns. There are nodes and antinodes in every standing wave pattern.

FAQs on Standing Wave

1. How Standing waves formed through string?

When two waves of the same frequency collide while moving in opposing directions through the same medium, standing waves are created. The nodes are constantly in the same place along the medium, giving the pattern the impression of being stationary. The fixed ends of the string is always a node for the standing wave. 

2. Do all standing waves carry nodes?

An alternating pattern of nodes and antinodes is always present in a standing wave pattern. A rope vibrating in a standing wave pattern is seen in the animation below. On the diagram, the nodes and antinodes are labeled.

3. What type of wave is formed through rope?

A standing wave is formed in a rope if there are two waves traveling in the opposite direction with same amplitude and frequency. When a standing wave is formed in a rope, then the fixed ends of the rope will have nodes with amplitude zero. 

4. What is the example of standing waves?

A basic illustration of a standing wave is a string plucked out of a guitar. Depending on the length of the string and how tight or thick it is, a plucked string generates a certain sound frequency. Only particular standing waves may develop on each string, resulting in only certain sounds being produced.

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