The discussion revolves around calculating the overall uncertainty of a derived quantity R, defined as R = (h² + l²) / 2h, where h and l are measurements with associated uncertainties. Participants are exploring the implications of these uncertainties on the final result.
Some participants have offered guidance on using differentials for uncertainty propagation and have raised questions about the clarity of the uncertainty values provided. There is an ongoing exploration of the relationships between actual and percentage uncertainties, with no explicit consensus reached yet.
Participants are navigating the complexities of uncertainty calculations, including the need for current values of h and l, and how to properly interpret and apply the given uncertainties. The discussion reflects a mix of understanding and confusion regarding the definitions and calculations involved.
<br /> <br /> Yeah those are the actual uncertainties in the values<br /> h = ±0.57% is the % uncertainty, where h is a measurement of length in m<br /> To get the uncertainty in h<sup>2</sup> you multiply the %uncertainty of h by 2 yeah?HallsofIvy said:Use the "differential"- R = (h2+l2)/2h dR= [(1- 2(h^2+ l^2))/h^2]dh+ (l/h)dl. Set dh and dl equal to the uncertainties in h and l respectively. You will need "current" values for h and l as well as for dh and dl. I do not understand you last values. Where you have "h = ±0.57%" do you mean the uncertainty in h (my "dh") rather than h itself? Also you have "h2=±1.14%" which is 2 times your h, not h squared.
You are confusing me by saying "actual uncertainty" at one point and "% uncertainty" at another- those are NOT the same thing. If h= 10, say, and the "actual uncertainty" (I would say "relative error") is 0.5 then the "percentage uncertainty" is (0.5)/(10)= 0.05= 5%. If f(x)= x2 then df= 2x(dx) The "actual uncertainty in f is 2 times the value of f time the "actual uncertainty" in x. The "percent uncertainty" in f is df/f. Dividing both sides of the previous equation by f, df/f= 2x(dx)/f= 2x(dx)/x2= 2(dx/x) so the percent uncertainty in x2 is 2 times the percent uncertainty in x.Ch3m_ said:Yeah those are the actual uncertainties in the values
h = ±0.57% is the % uncertainty, where h is a measurement of length in m
To get the uncertainty in h2 you multiply the %uncertainty of h by 2 yeah?