Experimental Methods 2014-15

*Prof Chris Haniff*

## Prerequisites

This course requires the material covered in the IA Physics and IA Maths for Natural Scientists courses, and exploits the ideas of Fourier theory that are more fully developed in the Mathematics options that run in parallel with this course in the Michaelmas term. Ideas of Fourier decomposition will be introduced, along with Fourier series, but they are covered more fully in the Mathematics option.

## Learning Outcomes and assessment

Physics is an empirical subject based on measuring physical phenomena. This course introduces techniques for putting together experiments and analysing their results. Many complex systems, ranging from telescopes to mobile phones, can often be understood in terms of a set of black boxes with simple interactions between them. This systems approach is particularly useful in experimental physics where the signal chain from the physical phenomenon under investigation to a measurement can involve many sequential and complex components such as transducers, amplifiers, filters and detectors.

The first part of this course explores this process – sometimes with reference to some of the experiments undertaken in the practical classes – while the second part introduces you to some of the essential material that a physicist needs to know so as to design experiments (including computational ones), to analyse data, and to evaluate other people’s results.

## Synopsis

**Systems:** Impedance and measurement. Operational amplifiers and filters. Positive and negative feedback with ideal and non-ideal amplifiers.

**Random errors:** examples, propagation, reduction with repeated sampling.

**Systematic errors:** examples, designs to reduce them (e.g. nulling), selection effects.

**Basic data handling**: taking and recording data. The right plot; error bars. Sampling, aliasing, Nyquist’s criterion. Digitization errors.

**Exclusion of unwanted influences:** filtering, phase-sensitive detection and lock-in amplifiers. Vibrational, thermal and electrical shielding.

**Probability distributions:** binomial, Poisson and Gaussian; central limit theorem; shot noise and Johnson noise.

**Getting the message across: **writing a scientific report and presenting results.

**Parameter estimation:** likelihood, inference and Bayes’ theorem, chi-squared, least-squares, hypothesis testing, non-parametric tests.

**BOOKS**

There are no books which cover the complete course syllabus, and so each lecture handout will be augmented with a set of supplementary notes. Reading these notes prior to the lectures will be helpful. The following books may be useful to refer to on certain aspects of the course:

*The Art of Electronics*, Horowitz P & Hill W (2nd edn CUP 1989)

*Analogue and Digital Electronics for Engineers*, Ahmed H & Spreadbury P J (CUP 1984)

*An Introduction to Experimental Physics*, Cooke C (CRC Press 1996)

*Practical Physics*, Squires G L (4th edn CUP 2001)

*Experimental Physics: Modern Methods*, Dunlap R A (OUP 1988)