Hanbury Brown and Twiss effect demonstrated for sound waves from a waterfall; an experimental, numerical and analytical study

Abstract

The Hanbury Brown and Twiss effect (HBT) is described by numerical and analytical modeling, as well as experimentally, using sound waves and easily available instrumentation. An interesting phenomenon that has often been considered too difficult to be included in standard physics studies at bachelor and master level, can now be introduced even for second year bachelor students and up. In the original Hanbury Brown and Twiss effect the angular size of the source (the star Sirius) was calculated by determining the distance between two detectors that lead to a drop in the cross-correlations in the signals from the detectors. We find that this principle works equally well by sound waves from a waterfall. This is remarkable, since we use a completely different kind of waves from the HBT case, the frequency of the waves differ by a factor $\sim 10^{12}$ and the wavelength as well as the angular extension of the source seen from the observer's position differ by a factor $\sim 10^{7}$. The original HBT papers were based on measurements of \emph{intensity} fluctuations recorded by two detectors and correlations between these signals. The starting point for the theory that explained the effect was therefore intensity fluctuations per see, and the theory is not easy to understand, at least not for an undergraduate physics student. Our starting point is descriptions of broadband waves at the amplitude level (not at intensity level) by numerical modeling. Important properties of broadband waves can easily be revealed and understood by numerical modeling, and time-resolved frequency analysis (TFA) based on Morlet wavelets turns out to be a very useful tool. In fact, we think it has been far too little attention to broadband waves in physics education hitherto, but the growth of use of numerical methods in basic physics courses opens up new possibilities.