Radioactive Decay: Audio Data Collection

Primus: Problems, Resources, and Issues in Mathematics Undergraduate Studies, Jul/Aug 2009 by Struthers, Allan

Abstract:

Many phenomena generate interesting audible time series. This data can be collected and processed using audio software. The free software package Audacity is used to demonstrate the process by recording, processing, and extracting click times from an inexpensive radiation detector. The high quality of the data is demonstrated with a simple statistical analysis.

Keywords: Audio, timet series, data, radioactive.

1. INTRODUCTION

Interesting audible time series are everywhere. For instance, popcorn popping, water dripping, traffic, crickets chirping, metronomes, and applause are easily recorded and a quick search on YouTube yields spring peepers (rhythmic, vocal spring frogs), pileated woodpeckers, and Gieger counter clicks.

The initial recordings are sometimes noisy but students can easily crop, reduce background noise, alter pitch/tempo, etc. using the straightforward manipulation tools in modern audio software to produce clean audio data. Using the same software students and faculty can extract and save the event (pops, drips, cars, or chirps as the case may be) times using event detection. With this process, users can automatically extract thousands of clear, repetitive, audible events from recordings up to an hour long. We will illustrate the process here with the free, well documented, frequently updated, and user friendly software Audacity [1] which is available for Windows, Mac, and Linux. Although many packages have similar features, most lack Audacity's reassuring visual confirmation of event detection.

In this article we use an inexpensive, military-surplus, Russian, Geiger counter and antique uranium-glass bowl to demonstrate how to record, process, and extract events (in this case clicks) using the silence detector in Audacity. This natural radioactivity is the prototype random process in many introductory texts, for an example see [2], and is drought of as a source of genuine random numbers, for an example see HotBits [3]. Students can explore the question "What does random sound like?" by collecting, hearing, and analyzing data from mis iconic process.

2. THE EXPERIMENT

The experiment is accessible, inexpensive, and safe. Russian military surplus radiation detectors (search for dosimeter) can usually be purchased on ?-bay for between $15 and $30. Background radiation levels will produce a rather sparse recording in most parts of the world. However, older gas lantern mandes contain radioactive thorium, vintage vaseline glass contains uranium, low-sodium salt substitute contains radioactive potassium, and granite countertops contain numerous radioisotopes. The presence of any of diese materials will produce suitably dense recordings and significantly sized data. Alternatively, a radioactive source and detector can probably be borrowed from a science department.

Natural radioactivity is the standard motivational example of a Poisson process because the physical reality (a large number of identical atoms each with a low decay probability) matches the defining mathematical axioms well. Moreover, Poisson processes are frequently the first time-series discussed because the defining mathematical properties are easily stated and the mathematical arguments establishing the exponential distribution of waiting times between events from the definition are clear and relatively simple.

As we will show, the radioactive decay data from a $15 detector fits both the defining properties and the exponential distribution of waiting times surprisingly well. A cautionary note about the perils and serendipitous scientific benefits of real data is revealed by a detailed examination of the waiting time distribution. In a finely binned histogram it is obvious that the inexpensive detector records fewer waiting times below 0.05 seconds than is predicted by the exponential distribution. The simple explanation is that all Geiger counters have a brief dead time after recording an event during which they miss subsequent events while the detector resets. This dead time is very short for an expensive, wall-powered, scientific detector but is apparently approximately 0.05 seconds for the $15, battery-powered ?-bay model.

2.1. Data Collection

To collect audio place the detector and microphone near the source (see Figure 1), record a few minutes of clicks with minimal background noise, and save the file in a standard audio format. Standard audio formats can be imported into Audacity and easily edited (crop, noise reduction, tempo alteration, pitch alteration, frequency filters are available) to produce clean data. Figure 2 is an Audacity Screenshot of a Geiger counter recording with clicks visible as vertical lines.

2.2. Event Time Extraction

The clicks can be extracted using the Audacity Silence Detector. Select the entire track (Select All on the edit menu) and choose Silence Finder from the analyze menu. Figure 3 is a Screenshot of a zoomed in Gieger counter recording with the silence finder panel. Set the Place Label slider to 0 seconds, set the Minimum Silence Duration down to 0.01 seconds (type in the box if the slider will not allow you to set it this low), and experiment with the Silence Level to capture all the visible clicks. Figure 3 is a screenshot of a zoomed in Gieger counter recording with the Silence Finder panel. Figure 4 is a Screenshot after running Silence Finder with the Export Labels panel open. The label track below the audio indicates all the clicks, literally the ends of the silences, that were detected. Although, it is not practical to confirm visually all the labels in a long recording a quick check in a few time segments is reassuring. Export Labels under the file menu saves the labels as a text file which can be directly imported into external programs. Each row in the file is a two decimal place accurate time in seconds followed by a tab and an S to indicate silence. There are numerous other event detection possibilities (including marking individual events) which set different labels.