Exploring the Physics of Waves

[fisico30]

waving around...

hello Forum,

a question about waves. First of all, to my understanding, a wave is a phenomenon that transports something (energy, mass...) from point A to point B.

That sounds a lot like convection to me, but the convection equation has a 1st order time derivative, while the wave equation has 2nd order time derivative.
Why the second derivative?

b) Isn't a wave just any function whose argument is (space $$\pm$$ speed*time)?
(actually two standing waves can form a traveling wave, and viceversa)

c) What if in the equation, instead of the Laplacian, there was a Laplacian or higher order? The equation would still be a wave equation...but with what difference?

And why does a first order time derivative represent gain or loss(say we want to add gain or loss to the equation)? That is not what we have in the convection equation...

Thanks!
fisico30

 

[eljose79]

Hello fisico30,

Thank you for your question about waves. You are correct in your understanding that a wave is a phenomenon that transports something (energy, mass, etc.) from one point to another. However, there are some important differences between waves and convection.

First, let's define what we mean by convection. Convection is the transfer of heat or mass through the movement of a fluid (such as air or water). This transfer occurs due to differences in temperature or density within the fluid. In contrast, waves can transport energy or mass through a medium without actually moving the medium itself.

Now, onto your questions about the wave equation. The second derivative in the wave equation is necessary because it represents the acceleration of the wave. This is important because waves are characterized by their ability to propagate and carry energy, which requires acceleration.

To answer your question about waves being any function whose argument is (space +/- speed*time), this is not entirely accurate. While this may be true for some types of waves, such as sinusoidal waves, it is not a universal definition. There are many different types of waves that can be described using various equations, and not all of them will have that form.

Regarding your question about using a higher order Laplacian in the wave equation, this would result in a different type of wave. The Laplacian is a mathematical operator that describes the rate of change of a quantity over space, so using a higher order would result in a more complex wave with different properties.

As for your question about adding gain or loss to the wave equation, this is not typically done in the context of waves. The wave equation is a model that describes the behavior of a wave in a medium, and adding gain or loss would change the fundamental properties of the wave. In contrast, the convection equation is specifically designed to include gain or loss, as it is describing the transfer of heat or mass through a medium.

I hope this helps clarify some of your questions about waves. Keep exploring and asking questions, as there is always more to learn about this fascinating phenomenon!

 

[charng]

Hello fisico30,

Thank you for your question about waves. I would like to provide some insights into the physics behind waves and address your questions.

Firstly, you are correct in your understanding that waves transport something (energy, mass, etc.) from one point to another. This is a fundamental property of waves and is what makes them so important in many areas of science and technology. However, there are different types of waves, such as mechanical waves (like sound waves) and electromagnetic waves (like light waves), and they can behave differently depending on the medium they are traveling through.

Regarding your question about the second order time derivative in the wave equation, this is due to the fact that waves have both amplitude and frequency. The second derivative represents the acceleration of the wave, which is related to its frequency. This is necessary to fully describe the behavior of a wave and understand how it changes over time.

In terms of the equation you mentioned with a higher order Laplacian, this could potentially describe a different type of wave with more complex behavior. However, the wave equation with a second order Laplacian is the most commonly used and well-studied equation for describing waves in various mediums.

Finally, your question about adding gain or loss to the equation is an interesting one. In the wave equation, the first order time derivative represents the rate of change of the wave, which can be affected by factors such as energy loss or gain in the medium. This is not the same as the convection equation, which describes the flow of a substance, and therefore has a different form.

I hope this helps to answer your questions about the physics of waves. If you have any further inquiries, please feel free to reach out. Keep exploring and learning about the fascinating world of waves!

Best regards,