Crossed Sines - Daniel Ludwigsen and Brad Roche

Fig. 6.11 from Russell's text should load here
Figure 6.11 from Introduction to Acoustics, Daniel Russell


In the discussion of critical bands, Dr. Russell includes this figure as an illustration of  how two pure sine tones (single-frequency tones) interact.  Outside the critical band, the tones are heard distinctly as they excite different parts of the basilar membrane in the cochlea.  If the frequency of one of the tones is swept through the frequency of the other, we hear first a "roughness" then "beating."  As the tone continues higher than the stationary tone, we go through another beating region and roughness, then hear two distinct tones once again.

The Tones

Hear the aural demonstration in this WAV file (25 seconds, 500 KB).
spectrograph of two tones crossing

The spectrograph of this WAV file shows the two single-frequency tones as they cross around 12.5 s.  The wavering that you hear just before and just after this is called beating, and arises from alternating constructive and destructive interference to give us high and low amplitude (loud and soft sound).  The roughness that you may hear is more subtle, and different people may respond differently. 

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Copyright Daniel O. Ludwigsen, 2005