1

I'm studying about the waves and the classical wave equation where I'm searching out the methods to check whether a function represents a wave or not, and I come up with this question.

Qmechanic
  • 201,751
senku ishigami
  • 81

1 Answers1

0

Most functions can be expressed as a sum of sines and cosines (waves) though the use of a Fourrier transform and are therefore wave like(a sum of waves is a wave).

So when exactly can we apply a Fourrier Transform ?

Well there are 3 conditions for a Fourier Series of a function to be exist: 1. It has to be periodic. 2. It must be single valued, continuous.it can have finite number of finite discontinuities. 3. It must have only a finite number of Maxima and minima within the period. 4. The Integral over one period of |f(X)| must converge. Each of them have Analytical proofs but let's discuss them using analogy.

Manu de Hanoi
  • 1,566
  • This may be true, but it doesn't answer the question. – garyp May 15 '21 at 13:58
  • I'm replying to the concern stated as "I'm searching out the methods to check whether a function represents a wave or not". If the method can be fourrier transformed, it represents a wave – Manu de Hanoi May 15 '21 at 16:05
  • will you also give answer to the direct question,"Is every function that satisfies classical wave equation, represent a wave?" – senku ishigami May 15 '21 at 19:28
  • Condition #1 kills your argument. Not every wave is periodic. – garyp May 16 '21 at 01:41
  • I believe you'd have to define what a wave is, cause if a wave can be anything then we are in trouble. – Manu de Hanoi May 16 '21 at 20:42
  • from wiki, wave equation : "The basic wave equation is a linear differential equation and so it will adhere to the superposition principle. This means that the net displacement caused by two or more waves is the sum of the displacements which would have been caused by each wave individually. In addition, the behavior of a wave can be analyzed by breaking up the wave into components, e.g. the Fourier transform breaks up a wave into sinusoidal components. " – Manu de Hanoi May 16 '21 at 20:48