Simple harmonic potentials & classical waves

In summary, a simple harmonic potential is a type of potential energy described by a harmonic oscillator function and characterized by quadratic increase in potential energy with distance from the equilibrium position. A classical wave is a disturbance that propagates through a medium without permanently displacing it, exhibiting periodic motion. These two concepts are closely related as classical waves can often be described using simple harmonic potentials, and the equations used to describe simple harmonic motion can also model the motion of particles in classical waves. Examples of simple harmonic potentials and classical waves can be found in natural and man-made systems, and they have various practical applications in fields such as engineering, physics, and music.
  • #1
gildomar
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2

Homework Statement



It's not a direct question, but it's an implied part of a larger question: can classical waves experience simple harmonic oscillator potentials, like a mass on a spring does?

Homework Equations





The Attempt at a Solution



I'm thinking no, since I can't come up with a scenario where classical waves would experience such a potential. The closest that I got the waves interacting with a parabolic dish, but I wouldn't really consider that an oscillator potential.
 
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  • #2
I can't think of one either.
 

1. What is a simple harmonic potential?

A simple harmonic potential is a type of potential energy that can be described by a mathematical function known as a harmonic oscillator. It is a special case of a more general type of potential energy called a quadratic potential. In simple harmonic potentials, the potential energy increases quadratically as the distance from the equilibrium position increases.

2. What is a classical wave?

A classical wave is a disturbance that propagates through a medium, such as air or water, without permanently displacing the medium. This means that the particles of the medium oscillate back and forth in a periodic motion, but their overall position remains relatively unchanged. Examples of classical waves include sound waves, water waves, and electromagnetic waves.

3. What is the relationship between simple harmonic potentials and classical waves?

Simple harmonic potentials and classical waves are closely related because they both exhibit periodic motion. In fact, classical waves can often be described using simple harmonic potentials, as in the case of a mass on a spring. Additionally, the motion of particles in a classical wave can be modeled using the same equations as those used to describe simple harmonic motion.

4. What are some real-life examples of simple harmonic potentials and classical waves?

Simple harmonic potentials and classical waves can be found in many natural and man-made systems. Some examples include the motion of a pendulum, the vibrations of a guitar string, the oscillations of a water surface, and the propagation of sound waves through air. These types of systems are characterized by a restoring force that is proportional to the displacement from an equilibrium position, leading to simple harmonic motion.

5. What are some applications of simple harmonic potentials and classical waves?

Simple harmonic potentials and classical waves have numerous practical applications in fields such as engineering, physics, and music. For example, they are used in the design of mechanical systems, such as car suspensions and shock absorbers, to create stable and efficient oscillatory motion. In physics, they are used to model the behavior of atoms in solids and to study the properties of electromagnetic radiation. In music, they are the basis for the production of different musical notes and tones.

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