Revision:Measurement 2

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8.1 Standards of measurement

8.1.1

Sine and Cosine rules - (both of which are in the data book).

The sine rule is:

Where the lower case letters are lengths of the sides of a triangle, and the upper case are the angles opposite these sides...this lets you work out stuff about triangles.

The Cosine rule is:

where , . and are as above. The letters can be rearranged or you can just relabel the triangle. The easiest way to remember it is as an extended version of pythag, with a correction added in, but it's in the data book, so I guess we don't have to remember it anyway.

8.1.2

Be able to use logs...This is something for maths really...but just briefly, to the base 10. in base ( is about 2.71...). Taking the log of both sides of an equation is the equivalent of reversing the effect of putting both sides to the power of the base. ie ...this needs to be done with some of the decay equations...but if you don't know it now...well...any decent maths book will explain it :)

8.1.3

Basically, the tricky thing here is identifying what the functions look like (often it's possible to graph it on a graphic calculator, but sometimes there are two variables, making things rather tricky. The amplitude of the resulting function will be the difference between the maximum and minimum values, which can be found by knowing where the sin and cos curves peak (and this can always be graphed). Usually, the easiest way to work anything else out it to graph each separate segment, then apply the transformations mentally (ie multiply the two curves together or whatever), and then think about the resulting graph...this is tricky (and I've never seen a question on it either)...does anyone have a better way ?

8.2 Graphical techniques

8.2.1

Using log scales...again, rather tricky to describe without proper diagrams...but again I seriously doubt there'll be any questions on it...anyone got a neat explanation ? :) Personally, I find it easier to do the transformations into a log scale (as the IB suggests you don't)...but that's just me

8.2.2

Basically, if a scale has been logged, then the unit must be put to the power of the base to compensate in any expression derived from the graph.

8.2.3

Similar to the SL section, except no we can use powers and reciprocals on log graphs as well as with 'normal' graphs.

8.3 Uncertainties and errors

8.3.1

The absolute value of uncertainty is just what's normally given...ie in 7.0±.5, the absolute uncertainty is 0.5. The relative uncertainty is 0.5/7, or 1/14 -- in general absolute uncertainty/value. Functions are basically just a bunch of operations lumped together, so the error just has to be worked through the function.

8.3.2

Carrying errors through a series of calculations is fairly simple...just remember to calculate the uncertainty at the end of each calculation, then carry this value and uncertainty on to the next.

8.3.3 : Problems caused by digital equipment

Quantization...this is caused by converting continuous analogue data into individual digital numbers.

Sampling frequency...the digital systems con only 'grab' a piece of data every x sec (let's say 0.01). If the data is changing significantly within this amount of time, then the sampled results will be almost random compared to the actual signal.

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