INTRO TO EXPERIMENTAL PHYS-LAB 1494/2699

Introduction to Experiment: 
Part 3 



Nate Saffold 
nas2173@columbia.edu



Office Hour: Monday, 5:30PM-6:30PM @ Pupin 1216

PHYS 1493/1494/2699: Introduction to Experiment – Part 32

Announcements

1. The lab sessions will start next week (February 6th). NOTE: The experiment will not follow the same order as in the lab manual. Refer to the preceptors’ website for the full calendar

2. 2nd quiz next week!

3. Download Mathematica/Excel, I will send a tutorial on how to download soon.

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Review: Error Propagation● Here are the rules for propagating error this semester!

− Addition/Subtraction:

− Multiplication by Constant (B is known exactly):

− Multiplication/Division:

− Exponents:

PHYS 1493/1494/2699: Introduction to Experiment – Part 3

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Review: Error Propagation● This is the general rule for error propagation, it will not lead you

astray! (But you will have to take some partial derivatives)

− Formula if f(x), i.e. f is only function of one variable

− Formula For Error Propagation for f(x,y,z):

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Step-by-step Error Propagation

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Step-by-step Error Propagation● Using the rules of error propagation can determine the error of any

function. Sometimes this may be easier than taking partial derivatives

● Any calculation can be broken down into a sequence of steps, each involving the following types of operation: ● Sums and Differences ● Products and Quotients ● Functions of one variable, i.e. sin(x), xn, ex, or ln(x)

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Example

PHYS 1493/1494/2699: Introduction to Experiment – Part 3

● If the quantities x, y, z and u are measured, each with uncertainty, how would you compute the error in q?

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Example

PHYS 1493/1494/2699: Introduction to Experiment – Part 3

● Find error in sin(u) ● Find uncertainty in product z*sinu ● Find uncertainty in difference y - z*sinu ● Find uncertainty in product x(y - z*sinu)

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Example

PHYS 1493/1494/2699: Introduction to Experiment – Part 3

● Find error in sin(u)

● Find uncertainty in product z*sinu

● Find uncertainty in difference y - z*sinu

● Find uncertainty in product x(y - z*sinu)

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Intermission● We want to determine the uncertainty in the mean of a sample:

● Each data point xi is drawn from a distribution with a standard deviation (i.e. uncertainty) equal to

● What is the uncertainty in the mean?

● But this means:

● This should look familiar!

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Defining Uncertainty Values● Typically, we define the uncertainty as half the precision of the

measurement scale we are using

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Defining Uncertainty Values● Typically, we define the uncertainty as half the precision of the

measurement scale we are using ● In the following scenario, what is the uncertainty in the length of

the pencil?

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Defining Uncertainty Values● Typically, we define the uncertainty as half the precision of the

measurement scale we are using ● In the following scenario, what is the uncertainty in the length of

the pencil?

● Since the ruler has millimeter precision, the uncertainty in our measurement is .5mm.

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Questions?

PHYS 1493/1494/2699: Introduction to Experiment – Part 3