Reflected wave equation

In summary, the equation of the reflected wave from a wall for a progressive wave represented by y = A[sin(wt - kx)] will be y = A1[sin(wt + kx)], with a possible phase change of pi depending on the density of the wall and the boundary conditions. The negative sign in the expression will be determined by the boundary conditions.
  • #1
Amith2006
427
2
Sir,
Consider a progressive wave represented by the equation,
y = A[sin(wt – kx)]
If it is reflected from a wall, what will probably be the equation of the reflected wave?
I think it is y = A1[sin(wt + kx)]
Is it right? Should a negative sign be given to the expression? Will there be a phase change of pi assuming the wall to be rigid boundary?
 
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  • #2
Amith2006 said:
Sir,
Consider a progressive wave represented by the equation,
y = A[sin(wt – kx)]
If it is reflected from a wall, what will probably be the equation of the reflected wave?
I think it is y = A1[sin(wt + kx)]
Is it right? Should a negative sign be given to the expression? Will there be a phase change of pi assuming the wall to be rigid boundary?

There will be a phase change of [itex]\pi[/itex] if the wall is of a denser medium than the incident medium. Since the wall is rigid, this is correct. [itex]A_{1}[/itex] is determined from considerations of boundary conditions. That will tell you whether there should be a minus sign or not. You don't have to "give" it a negative sign.
 
  • #3


Yes, your equation is correct. The reflected wave will have the same amplitude as the incident wave, but the sign of the wave vector (k) will be opposite, resulting in a reflected wave traveling in the opposite direction. Therefore, the equation for the reflected wave will have a positive sign for kx, as shown in your equation.

As for the phase change, it depends on the type of boundary the wall represents. If the wall is a rigid boundary, there will be a phase change of pi (180 degrees) as the wave reflects off of it. This means that the reflected wave will be shifted by half a wavelength compared to the incident wave. However, if the wall is a soft boundary, there may not be a phase change or it may be different depending on the properties of the boundary.
 

What is the "Reflected Wave Equation"?

The Reflected Wave Equation is a mathematical equation used to describe the behavior of waves when they encounter a boundary or interface between two different materials or mediums. It shows how the incident wave is reflected back when it encounters the boundary.

What is the formula for the Reflected Wave Equation?

The formula for the Reflected Wave Equation is R = (Z2 - Z1) / (Z2 + Z1), where R is the reflection coefficient and Z1 and Z2 are the impedances of the two materials or mediums.

What does the Reflected Wave Equation tell us about waves?

The Reflected Wave Equation tells us about the amplitude and direction of the reflected wave when it encounters a boundary. It also shows us how the reflected wave is affected by the properties of the two materials or mediums.

Is the Reflected Wave Equation applicable to all types of waves?

Yes, the Reflected Wave Equation is applicable to all types of waves, including electromagnetic waves, sound waves, and water waves. It can also be used to describe the behavior of waves in different mediums, such as air, water, or solids.

How is the Reflected Wave Equation used in real-world applications?

The Reflected Wave Equation is used in various real-world applications, such as in the design of acoustic materials, sonar technology, and seismic imaging. It also plays a crucial role in understanding and predicting the behavior of waves in different environments, which is essential in fields like oceanography and geology.

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