Small firearms can create sound levels exceeding the safe threshold of human hearing with even one shot. Understanding how the sound propagates will lead to better range and military drill design. This thesis describes errors associated with different predictive interpolation models for the M16A4. Before directly discussing potential sources of error, the thesis first seeks to validate the data acquired. This is done through waveform inspection with a focus on shot-to-shot consistency. Finding the standard deviation in level between a 10-shot volley provides a good baseline with which other sources of error can be compared to. For both peak and 8-hour A-weighted equivalent levels, the deviation tended to be 1-1.2 dB. With this constraint in mind, the thesis then discussions potential error of measurements along the radial arc. By comparing nearest neighbor microphones with measured values, it was determined that a finer resolution behind the shooter is most relevant. Second, radial propagation was plotted to justify potential decay rates for further plotting. A model of spherical spreading is reasonable, but overestimates the level at farther distances e.g. 50 m. Lastly the thesis focuses on interpolation mapping to predict levels around the range. The baseline model was created using a Cartesian interpolation scheme that uses ghost points to help limit potential artifacts. Leave-one-out analysis highlighted a necessity of microphone placement behind the shooter and other less important microphones. Use of symmetry across the firing direction provides excellent results, generally below the 1 dB standard deviation. In the end, a best-practices guideline is given, which reduces number of required microphones by half. Through these analyses, future measurements will be more effective in microphone placement. With these level maps, one will also be able to better determine potential hearing risks associated with small firearm use and even avoid them through better drill.



College and Department

Physical and Mathematical Sciences; Physics and Astronomy



Date Submitted


Document Type





Acoustics, rifle, gunshot, noise, interpolation, modelling, leave-one-out, symmetry, error, ghost points