Three independent laboratory groups measure the speed of sound in air at the same…

PHYSICS · Subjective · Fermi University Physics · Scientific Practice & Experimental Methods · Data analysis and model fitting in the laboratory · Data analysis and model fitting in the laboratory

Measurement and Method, Ch Graphs, straight lines and least squares

Problem

Three independent laboratory groups measure the speed of sound in air at the same temperature by different methods and report: Group 1 (resonance tube):

343.2 \pm 0.5\,\mathrm{m\,s^{-1}}

; Group 2 (echo timing):

342.6 \pm 0.8\,\mathrm{m\,s^{-1}}

; Group 3 (Kundt's tube):

343.9 \pm 0.3\,\mathrm{m\,s^{-1}}

. The three results are independent, each using a different instrument and operator. (a) Check that the three results are consistent, using Chapter 7's consistency ratio for each pair, and state why they should then be combined by a weighted mean rather than a simple average. (b) Compute the weighted mean speed of sound

\bar v_{\rm w}

and its uncertainty

u(\bar v_{\rm w})

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