Why is the general form of the wave equation a second order partial derivative?

In summary, the second order partial derivative form of the wave equation is because it is a more accurate description of a wave.
  • #1
Michael95
4
0
When I deduct the the general form of wave equation, I noticed it has a second order partial derivative form. I am wondering why wave equation has a second order partial derivative form nor a first order partial derivative form?
 
Physics news on Phys.org
  • #2
Greetings,
Sorry, I have to ask...
Could you be more specific about "wave equation"?
 
Last edited:
  • #3
Michael95 said:
When I deduct the the general form of wave equation, I noticed it has a second order partial derivative form. I am wondering why wave equation has a second order partial derivative form nor a first order partial derivative form?

@Michael95 -- Welcome to the PF. If you wanted your thread moved, you should have clicked the Report button and asked the Mentors to move it. I have deleted your other thread, so this thread here can continue. :smile:
 
  • #4
berkeman said:
@Michael95 -- Welcome to the PF. If you wanted your thread moved, you should have clicked the Report button and asked the Mentors to move it. I have deleted your other thread, so this thread here can continue. :smile:
Aha, now we are talking...
 
  • #5
berkeman said:
@Michael95 -- Welcome to the PF. If you wanted your thread moved, you should have clicked the Report button and asked the Mentors to move it. I have deleted your other thread, so this thread here can continue. :smile:
Ha, I see. I am just join PF few minute ago. Thank you for tip.
 
  • #6
I have upload a picture. There is my deduction process. I wondering why wave equation has a second order partial derivative form?
 

Attachments

  • DSC_0002.JPG
    DSC_0002.JPG
    31.3 KB · Views: 530
  • #7
Michael95 said:
I have upload a picture. There is my deduction process. I wondering why wave equation has a second order partial derivative form?
I think because it is boring...Laughing out loud Click me fast!. (Take your time)[Need anything else?]
 
Last edited:
  • Like
Likes berkeman
  • #8
ToBePhysicist said:
I think because it is boring...Laughing out loud Click me fast!. (Take your time)[Need anything else?]
I see. The first oder wave equation can not perfectly describe a wave. Thank you for link.
 
  • #9
Michael95 said:
I see. The first oder wave equation can not perfectly describe a wave. Thank you for link.
Glad I helped ^_^
 

1. What is the general form of the wave equation?

The general form of the wave equation is a mathematical formula that describes the behavior of waves. It can be written as ∂²u/∂t² = c²∇²u, where u represents the wave function, t represents time, c is the speed of the wave, and ∇² is the Laplace operator.

2. What does the wave equation represent?

The wave equation represents the propagation of a wave through a medium. It describes how the wave function changes over time and space, and how it is affected by the properties of the medium it is travelling through, such as density and elasticity.

3. What are the variables in the general form of the wave equation?

The variables in the general form of the wave equation are u (wave function), t (time), c (wave speed), and ∇² (Laplace operator). These variables can be adjusted to model different types of waves and their behavior in various mediums.

4. How is the wave equation used in science and engineering?

The wave equation is used in many fields of science and engineering to study and predict the behavior of waves. It is commonly used in fields such as acoustics, optics, electromagnetics, and seismology. It also has applications in areas such as signal processing, medical imaging, and quantum mechanics.

5. What are the assumptions made in the general form of the wave equation?

The general form of the wave equation makes several assumptions, including that the medium is homogeneous (uniform throughout), isotropic (properties are the same in all directions), and linear (obeys the principle of superposition). It also assumes that there are no sources or sinks of energy within the medium and that energy is conserved as the wave propagates.

Similar threads

  • Other Physics Topics
Replies
8
Views
2K
  • Other Physics Topics
Replies
14
Views
2K
  • Differential Equations
Replies
7
Views
2K
  • Differential Equations
Replies
1
Views
1K
Replies
1
Views
484
Replies
3
Views
1K
  • Calculus
Replies
3
Views
2K
  • Introductory Physics Homework Help
Replies
15
Views
1K
Replies
17
Views
1K
Replies
5
Views
760
Back
Top