Superposition Of Transverse Waves.

In summary, when two waves traveling in opposite directions superpose in a thread, the shape of the thread becomes flat. This may seem like there is no energy stored, but the energy is actually stored in the speed of the wave oscillation and the velocity of the points on the wave. This is explained in detail in the AJP paper "What happens to energy and momentum when two oppositely-moving wave pulses overlap?" by N. Gauthier. The paper can be found in the American Journal of Physics, volume 71, page 787, published in 2003.
  • #1
Shan Ravi
11
0
When two waves traveling in opposite direction say in a thread, superpose the shape of the thread becomes flat. Where is the energy stored in the thread now. When a single is travelling, we say energy is stored as potential energy. But here there is no displacement of the thread in the vertical direction. So, there should be no energy stored. But they emerge out as two different full waves... where did this energy it derived from again?
 
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  • #2
Shan Ravi said:
When two waves traveling in opposite direction say in a thread, superpose the shape of the thread becomes flat. Where is the energy stored in the thread now. When a single is travelling, we say energy is stored as potential energy. But here there is no displacement of the thread in the vertical direction. So, there should be no energy stored. But they emerge out as two different full waves... where did this energy it derived from again?

The "energy" here is not just in the displacement of the wave oscillation, but also on the speed that it has. So even when there is a destructive interference, that is occurring only instantaneously for a traveling wave, and that points is still having a velocity, only it has zero displacement from the equilibrium point.

There is a very good and complete treatment of this issue in a AJP paper:

"What happens to energy and momentum when two oppositely-moving wave pulses overlap?", N. Gauthier, Am. J. Phys. v.71, p.787 (2003).

Zz.
 
  • #3
But the speed it has also traveling normally (I mean before superposing). So do you mean to say that the speed of the transverse vibration of the particles increases during superposition?

By the way, where can I read the AJP paper?
 

1. What is superposition of transverse waves?

Superposition of transverse waves is a phenomenon in which two or more transverse waves overlap and combine to form a resultant wave. This is possible because transverse waves move perpendicular to the direction of their oscillations, allowing them to interact and create more complex patterns.

2. How does superposition affect the amplitude of a wave?

When two waves with the same frequency and amplitude are superimposed, they will create a resultant wave with an amplitude equal to the sum of their individual amplitudes. However, if the waves have different amplitudes, the resultant wave will have an amplitude somewhere between the two.

3. What is the principle of superposition?

The principle of superposition states that when two or more waves meet at a point in space, the resulting displacement at that point is equal to the sum of the individual displacements caused by each wave. This principle applies to all types of waves, including transverse waves.

4. How does superposition affect the wavelength of a wave?

When two waves with different wavelengths are superimposed, the resulting wave will have a wavelength that is somewhere between the two original wavelengths. If the waves have the same wavelength, the resultant wave will also have that same wavelength.

5. What is an interference pattern and how is it related to superposition of transverse waves?

An interference pattern is a pattern created when two or more waves superimpose and create regions of constructive and destructive interference. This pattern is a result of the principle of superposition and can be seen in many natural phenomena, such as ocean waves and light waves.

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