The propagation speed of a shock or detonation wave in a shock or detonation tube is usually determined by a time-of-flight method by dividing the distance between two transducers with the propagation time of the disturbance signal. Some arbitrariness is inherent in determining the propagation time by this method. A new method based on Haar and Morlet wavelet transforms is reported. The method was tested against a step and a decaying spike with added noise, which are representative of shock and detonation waves. The wavelet methods can be applied to the step discontinuity provided that the SNR ratio is good. The wavelet methods worked very well for the decaying spike in the presence of noise.