The superposition of two sine waves with similar frequencies f 1 and f 2 (blue and green) linearly causes an interference frequency sinusoid at the sum frequency (f 1 + f 2 )/2 10 (orange) and another sinusoid which is the envelope of (f 1 + f 2 )/2 modulated at difference frequency (f 1 − f 2 )/2. The Fourier transform contains only the two frequencies f 1 and f 2 . Picture taken from [31].

Contexts in source publication

Context 1

... two similar sine waves oscillating at f 1 and f 2 (colored blue and green, respectively, in Figure 1) are linearly superposed. Due to constructive and destructive interference in their dynamically evolving phase relation, the amplitude periodically increases and decreases and does so with a frequency (colored orange in Figure 1) that is the sum frequency of f 1 and f 2 . ...

Context 2

... two similar sine waves oscillating at f 1 and f 2 (colored blue and green, respectively, in Figure 1) are linearly superposed. Due to constructive and destructive interference in their dynamically evolving phase relation, the amplitude periodically increases and decreases and does so with a frequency (colored orange in Figure 1) that is the sum frequency of f 1 and f 2 . As long as no non-linear medium is distorting the superposition, no signal is generated at the sum frequency. ...

Context 3

... Fourier transform of the time domain to the frequency domain only shows the two original frequencies f 1 and f 2 , and thus this is no new acoustic signal yet. Likewise, the difference frequency (colored red in Figure 1) is not appearing in the Fourier transform, just the intensity oscillation in the time domain. To arrive at the generation of a sum and a difference frequency signal, a non-linear distortion needs to occur as is shown in Figure 2. The mathematical function describing the mixing in the non-linear medium, the so-called transfer function, needs to be of quadratic order or higher; that is, it must contain exponents that are at least quadratic. ...