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Wave is an energy transport phenomenon. The wave traveling in a medium transports energy along a medium without transporting matter. The amount of energy carried by a wave is related to the amplitude of the wave. A high energy wave is characterized by high amplitude and a low energy wave is characterized by low amplitude.
The energy transported by a wave is directly propertional to the square of the amplitude of the wave. This energy-amplitude relationship may be expressed as:
For a stretched string the energy is given by,
E = ½ (mω^2A^2)
The Principle Of Superposition:
The principle of superposition may be applied to waves whenever two (or more) waves traveling through the same medium at the same time. The two waves having same frequency when superpose, the net displacement of the medium at any point in space or time, will be simply the sum of the individual wave displacements. This is true of waves which are finite in length (wave pulses) or which are continuous sine waves. Thus, the principle of superposition of waves states as follows:
“If two or more traveling waves are moving through a medium, the resultant wave function at any point is the algebraic sum of the wave functions of the individual waves.”
The waves which obey this principle are called the linear waves and are generally characterized by small amplitudes. The waves which do not obey this principle are called nonlinear waves and are often characterized by large amplitudes. It must be noted that two traveling waves can pass through each other without being destroyed or even altered.
Let us consider two waves having wave functions y1 and y2 respectively. When the two waves start overlapping the resulting complex wave is y1+y2. The combination of waves in the same region of space to produce a resultant wave is called interference.
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Waves and Optics