- #1
mrausum
- 45
- 0
For a string fixed at x=0 and free at x=l I know [tex]\frac{dy}{dx}(l,t)=0[/tex] (d's are meant to be partials) but what is the other boundry associated with the end of the string? Is the second derivative also equal to 0?
Boundary conditions are the set of rules that govern the behavior of a wave that is fixed at one end. These conditions determine how the wave will behave at the fixed end and how it will interact with the surrounding medium.
Boundary conditions are important because they help us understand how the wave will propagate and how it will interact with its surroundings. They also allow us to make predictions about the behavior of the wave under different conditions.
Some common boundary conditions for waves fixed at one end include: no displacement at the fixed end, no force at the fixed end, and no velocity at the fixed end. These conditions are based on the physical constraints of the system and the properties of the medium.
Boundary conditions can affect the speed of the wave by changing the way it interacts with the medium. For example, if the fixed end is rigid, the wave may reflect back with the same speed. However, if the fixed end is free to move, the wave may reflect back with a different speed.
Yes, boundary conditions can be changed for a wave fixed at one end. This can be done by altering the physical properties of the system, such as changing the fixed end from rigid to free, or by changing the properties of the medium, such as changing the density or elasticity. However, the specific boundary conditions will depend on the specific system and cannot be arbitrarily changed.