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

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SUMMARY

The general form of the wave equation is a second order partial derivative because it accurately describes wave propagation, capturing both spatial and temporal changes. First order wave equations fail to encapsulate the necessary dynamics of wave behavior, leading to incomplete representations. This discussion highlights the importance of second order derivatives in modeling physical phenomena such as sound and light waves.

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  • Understanding of second order partial derivatives
  • Familiarity with wave mechanics
  • Basic knowledge of differential equations
  • Concept of wave propagation
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  • Study the derivation of the wave equation in physics
  • Explore applications of second order partial derivatives in engineering
  • Learn about the differences between first and second order differential equations
  • Investigate numerical methods for solving wave equations
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Students and professionals in physics, engineering, and applied mathematics who are interested in understanding wave behavior and the mathematical foundations of wave equations.

Michael95
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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?
 
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Greetings,
Sorry, I have to ask...
Could you be more specific about "wave equation"?
 
Last edited:
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:
 
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...
 
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.
 
I have upload a picture. There is my deduction process. I wondering why wave equation has a second order partial derivative form?
 

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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?]
 
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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.
 
Michael95 said:
I see. The first oder wave equation can not perfectly describe a wave. Thank you for link.
Glad I helped ^_^
 

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