Abstract: The inverse problem for the one-dimensional acoustic wave equations is discussed.For the inverse problem to determine acoustic impedance from impulse response,sufficient condition and necessary condition are obtained for the wellposedness.These conditions are very simple and can be verified easily in numerical computation.For the inverse problem to determine acoustic impedance from wavelet response,it's usually illposed.The detailed analysis indicates that the more smooth the wavelet is,the more illposed the inverse problem is.

Key words: wave equation, inverse problem, stability