Measurement of the Speed of Sound in Air
Physics 1 Experiment #4: “Measurement of the Speed of Sound in Air” Measurement of the Speed of Sound in Air Write-up The data on the hand drawn graph, previously shown, fits that of a straight line; this means that there is a linear relationship between the dependent (position) and independent (time) variables. The value of the slope of the line determined by hand is the same as the value obtained from the linear regression done with the calculator because the points chosen were as precise as the graph obtained from excel.
The experimental velocity obtained from calculating the slope of the graph of position vs. time measured in lab was found to be: Vexp=34. 526 cm/ms The distance(cm) a sound pulse will travel in a time period of 0. 50 ms is calculated by doing the following: d=d0+V0t+12at2 d=0+V0t+0 d=34. 526cmms*0. 50 ms = 17. 263 cm A light pulse with the speed of 3. 00*10^8 will travel in 0. 50 ms a distance of : 3. 00*108ms*0. 0006214 miles1 m=x miles0. 50 ms*1000 ms1 s=93. 21 miles An experimental measurement with little or no systematic error is said to be of high accuracy.
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An experimental measurement with little or no random error is said to be of high precision. The Vaccepted = 346. 98 m/sec does not fall within the interval determined by the limits of the precision, as the following is not true for this experiment: ±? V=VexpSDMX ±? V=34. 526cmms0. 063cm61. 362cm=0. 035cmms Vacc-Vexp ? ?Vexp 1. 72ms? 0. 35ms In the above formula the error in time can be ignored as the error is associated with consistently centering the sharp peak of the voltage trace on the oscilloscope’s 0.
50 ms vertical grid lines. Furthermore, the reason Vaccepted did not fall within the interval determined by the limits of our experimental error determined before, is due to systematic error, which can be a consequence of not accounting for a temperature variable in the tube. In fact if there was a temperature dependence in the tube , the temperature that would be responsible for the lack of precision would be as follows: Vexp=332. 1171+TC273. 15=345. 26 TC=22. 05 ?
One can state that as a consequence of this experiment that the accepted speed of sound can be measured , with high precision , when taking into account all factors including temperature for the limitations in my claims are due to the systematic error in the system, otherwise the experimental value would be more precise when compared to the accepted value. Finally as compared to the accepted value of 346. 975 m/s , the experimental value found was 345. 3±0. 4 ms