The wave equation in classical physics is considered to be an important second-order linear partial differential equation to describe the waves. The wave equation arises in fields like fluid dynamics, electromagnetics, and acoustics. D’Alembert discovered the one-dimensional wave equation in 1746, after ten years Euler discovered the three-dimensional wave equation.
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One Dimensional Wave Equation Derivation
Consider the relation between Newton’s law that is applied to the volume ΔV in the direction x:
Where,
F: force acting on the element with volume ΔV
Above equation is known as the equation of motion.
Where,
K: bulk modulus
Rewriting the above equation:
Where,
c: velocity of sound given as
Thus, above is the one-dimensional wave equation derivation.
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Related Physics articles:
Wave | Derivation Of Schrodinger Wave Equation | Equation of Motion | Newton’s Law |
This video below explains the general wave equation, phase, and the motion of particles of the wave
![](https://cdn1.byjus.com/wp-content/uploads/2021/04/Wave-Equation.jpeg)
Frequently Asked Questions – FAQs
Who discovered the one-dimensional wave equation?
D’Alembert discovered the one-dimensional wave equation in the year 1746.
Who discovered the three-dimensional wave equation?
What is the formula to find the velocity of sound (c)?
Velocity of sound is given by the formula :
Can Waves exist in two or three dimensions?
State true or false: a water wave is a two dimensional wave.
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