How the mathematical wave equation was derived

In summary, the mathematical wave equation originated from the study of sound and light waves and was first derived by mathematician Jean le Rond d'Alembert in the 18th century. It is significant because it allows us to describe and understand various types of wave phenomena in a quantitative manner, and is derived using mathematical principles and the study of wave behavior in different mediums and boundary conditions. Real-world applications of the mathematical wave equation include acoustics, optics, electromagnetics, seismology, and various technologies such as radar, ultrasound imaging, and sonar.
  • #1
Ercross
1
0
Please, I've been unable to comprehend how the mathematical wave equation was derived.. Please can anyone explain it to me...
 
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  • #2
Ercross said:
Please, I've been unable to comprehend how the mathematical wave equation was derived.. Please can anyone explain it to me...

You'll have to tell us more before we can help. Show us the derivation you're having trouble with, and tell us at which point you're getting stuck, and we may be able to help you through it.
 
  • #3
The first minutes in this video has an excellent and clear derivation:
 

1. How did the concept of the mathematical wave equation originate?

The concept of the mathematical wave equation originated from the study of sound and light waves. Scientists observed that these waves could be described by a mathematical equation, and this led to the development of the wave equation.

2. Who first derived the mathematical wave equation?

The mathematical wave equation was first derived by mathematician Jean le Rond d'Alembert in the 18th century.

3. What is the significance of the mathematical wave equation?

The mathematical wave equation is significant because it allows us to describe and understand various types of wave phenomena, such as sound and light, in a quantitative manner.

4. How is the mathematical wave equation derived?

The mathematical wave equation is derived using mathematical principles, such as differential equations and the principle of superposition. It also involves studying the behavior of waves in various mediums and boundary conditions.

5. What are some real-world applications of the mathematical wave equation?

The mathematical wave equation has numerous real-world applications, including in fields such as acoustics, optics, electromagnetics, and seismology. It is also used in technologies such as radar, ultrasound imaging, and sonar.

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