Analyzing the acoustic beat with mobile devices

In this column, we have previously presented various examples of how physical relationships can be examined by analyzing acoustic signals using smartphones or tablet PCs.^1–3 In this example, we will be exploring the acoustic phenomenon of small beats, which is produced by the overlapping of two tones with a low difference in frequency Δf. The resulting auditory sensation is a tone with a volume that varies periodically. Acoustic beats can be perceived repeatedly in day-to-day life and have some interesting applications. For example, string instruments are still tuned with the help of an acoustic beat, even with modern technology. If a reference tone (e.g., 440 Hz) and, for example, a slightly out-of-tune violin string produce a tone simultaneously, a beat can be perceived. The more similar the frequencies, the longer the duration of the beat. In the extreme case, when the frequencies are identical, a beat no longer arises. The string is therefore correctly tuned. Using the Oscilloscope app,⁴ it is possible to capture and save acoustic signals of this kind and determine the beat frequency $fS$ of the signal, which represents the difference in frequency Δf of the two overlapping tones (for Android smartphones, the app OsciPrime Oscilloscope can be used).