Machine-translated by Google. Questions are authored in English.
Top

Discussion

D'Alembert's solution of the one-dimensional wave equation has the form

  • A.\( f(x)\cos ct + g(x)\sin ct \)
  • B.\( f(x - ct) \) alone
  • C.\( f(x - ct) + g(x + ct) \)
  • D.\( f(x - ct)\,g(x + ct) \)

Answer: C

The two arbitrary functions represent disturbances travelling in opposite directions without change of shape:

\[ y(x,t) \;=\; f(x - ct) + g(x + ct). \]

A single function would describe a wave running one way only, which cannot meet two initial conditions, and a product would not satisfy the equation at all

No comment is present. Be the first to comment.
Loading…

Post your comment

Please log in or register to post a comment.