Which of the following functions represent a stationary wave? Here a, b and c are constants: 

A stationary wave is characterized by a function of type $\mathrm{y}=\mathrm{f}\left(\mathrm{t}\right) \mathrm{g}\left(\mathrm{x}\right)$. Hence, choices (1) and (2) represent a stationary wave. Choice (4) is superposition of two oppositely travelling waves of the same amplitude and same frequency, which gives rise to a stationary wave. Hence choice (4) also represents a stationary wave.