(a) Which of the following functions could represent a traveling wave?

(i) \(A \cos (k x+\omega t)\)

(ii) \(e^{-k|x-c t|^{2}}\)

(iii) \(b(x-c t)^{2} e^{-x}\)

(iv) \(-\left(b^{2} t-x\right)^{2}\)

(b) Which of the following functions can be made to represent a traveling wave?

(i) \(x /\left(1+b x^{2}\right)\)

(ii) \(x e^{-k x}\)

(iii) \(x^{2}\)