For a string clamped at both ends, which of the following wave equation is valid for a stationary wave set…

For a string clamped at both ends, which of the following wave equation is valid for a stationary wave set up in it? (Origin is at one end of string)
  1. $y = A \sin kx \sin \omega t$
  2. $y = A \cos kx \sin \omega t$
  3. $y = A \cos kx \cos \omega t$
  4. All of the above

Solution

Node should be at $x = 0$. This is possible when $A_x = A \sin kx \sin \omega t$.

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