How Do You Solve the Wave Equation on a Half-Line?

In summary, the conversation discusses the process of finding a singularity using equations (31) and (32) and plugging in values to get the equation u(x,t) = 1 for x > ct and u(x,t) = 0 for 0 < x < ct. The person asks for feedback on this method and expresses confusion about finding a singularity with an answer of 1 and 0.
  • #1
sarahisme
64
0
lol my head is about to explode! :P

i think this is similar to a previous question i asked but i can't quite get it none the less...

http://img137.imageshack.us/img137/7796/picture11gf9.png

now what i did was to following this :

http://img100.imageshack.us/img100/951/picture12yv1.png

then using equations (31) & (32) from that i just plugged in the values and got:

u(x,t) = 1 for x > ct and u(x,t) = 0 for 0 < x < ct

how does this look to you intelligent mathematically inclined people? :S

Sarah :)
 
Last edited by a moderator:
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  • #2
but then how do you find a singularity when you have an answer of 1 and 0? :S
 

FAQ: How Do You Solve the Wave Equation on a Half-Line?

What is the wave equation on a half-line?

The wave equation on a half-line is a partial differential equation that describes the propagation of waves in an infinite medium that is confined to one side of an imaginary line. It is commonly used in physics and engineering to model phenomena such as sound and electromagnetic waves.

What are the boundary conditions for the wave equation on a half-line?

The boundary conditions for the wave equation on a half-line are that the wave amplitude must approach zero as the distance from the line approaches infinity. This means that the wave is confined to one side of the line and does not continue indefinitely.

What is the significance of the half-line in the wave equation?

The half-line in the wave equation is an imaginary boundary that separates the wave from the infinite medium. It allows us to model waves that are confined to one side of the boundary and do not continue indefinitely.

How is the wave equation on a half-line solved?

The wave equation on a half-line can be solved using various mathematical techniques such as Fourier transforms, separation of variables, and Laplace transforms. The specific method used depends on the boundary conditions and the type of wave being modeled.

What are some real-world applications of the wave equation on a half-line?

The wave equation on a half-line has many practical applications in fields such as acoustics, electromagnetics, and seismology. It is used to study the behavior of sound waves in rooms, electromagnetic waves in waveguides, and seismic waves in Earth's crust.

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