Measuring sound velocity from a P-T graph?

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SUMMARY

The discussion focuses on measuring sound velocity using a position-time (P-T) graph. The slope of the graph represents the velocity of sound, which can be calculated by dividing the total distance traveled by the sound pulse by the time of flight. It is emphasized that multiple measurements improve accuracy, and in non-dispersive media, the group velocity equals the phase velocity. The importance of varying distances and corresponding times for precise calculations is also highlighted.

PREREQUISITES
  • Understanding of basic physics concepts related to sound propagation
  • Familiarity with graph interpretation, specifically position-time graphs
  • Knowledge of group velocity and phase velocity in wave mechanics
  • Experience with experimental measurement techniques in physics
NEXT STEPS
  • Research methods for measuring sound velocity in different media
  • Learn about the differences between group velocity and phase velocity
  • Explore techniques for improving measurement accuracy in experiments
  • Study the principles of non-dispersive versus dispersive media
USEFUL FOR

Students in physics, researchers in acoustics, and professionals involved in sound measurement and analysis will benefit from this discussion.

apeldoorn
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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.
 
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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.
 

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