Measuring sound velocity from a P-T graph?

[apeldoorn]

I don't have any specific numerical values for this, as it's a general question, but hopefully I explain it well enough using only words:

If you plot a graph of position vs. flight time (of a sound pulse, for example), what is the slope of that graph going to be? (That is, what does the slope represent?)

Also, if you were to calculate the slope of a position-time graph, how would you determine the velocity of sound from that calculated information? (I believe that you can theoretically do that, right?) I've heard that can't you calculate the velocity of sound by taking a single measurement and dividing the time of flight into the total distance the sound pulse travel, but I'm not exactly clear as to why.

If anyone has any response to either of those questions, I'd very much appreciate your insight.

 

[nasu]

You can measure speed of sound in a medium by measuring propagation time of a pulse over a known distance. This will be the group velocity. For a non-dispersive medium it will be equal to the phase velocity as well.
As for any measurement, it is better to use several measurements rather than just one.
You can vary the distance and measure the corresponding times, for example from the slope of the d-t graph representing your results.