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Let's say I have real-life specimens of isotropic solid materials I want to investigate some properties of. Through my setup I'm able to send mechanical wave pulses into one cylindrical bar of the material and record what happens at some distance from the wave source along the axis.

Is there a standard method to perform velocity determination? Put it another way: are you aware of some widely accepted way in the literature to treat the output signal of such experiments (what to look for etc.), in order to gain knowledge about the speed of sound?

Of course as mechanics 101 tells us, the way to go would be: dividing the distance between the source and the measurement device by the time interval between the instant I send a signal and the instant the output pulse is recorded. But as you can imagine, there is no such thing as an "output pulse": the output signal does not resemble the one I sent in in the first place at all, and this happens due to various effects including reflections at the boundaries.

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If you can set up a standing wave in your material, introduce a high amplitude, low frequency signal into one end of the sample. Increase frequency until you get resonance. The fundamental frequency will occur at 1/2 of a wavelength (the length of your sample), which should correspond to the first resonance that you encounter as you increase frequency. The frequency will be known based on the equipment that you are using, so you can use the formula v = frequency x wavelength to calculate the velocity in the material.

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