# Ultrasonics – Sound – Beat Frequencies

The way in which sound sources operating at the same frequency combine to produce constructive and destructive intereference was discussed in a preceding blog.  In today’s blog, we will explore how sounds of two different frequencies combine to produce beat frequencies.

Two sound sources operating in phase at the same frequency produce reinforcement or constructive interference resulting in higher amplitude.  Sources operating at the same frequency but out of phase produce destructive interference which results in lower amplitude or, in a perfect example, no amplitude at all as the two sounds totally cancel each other out.  Two sound sources operating at different frequencies, however,  produce alternating zones of constructive and destructive interference with effects ranging from beneficial to disasterous.

The following illustration shows how sounds at two different frequencies combine.

The upper sound source is operating at frequency F1 Hz while the lower is operating at frequency F1 – 3 Hz.  The darker areas with more definition are regions where constructive interference is taking place.  The lighter areas where there is more blur than definition represent regions where destructive interference is taking place.  This interaction results in a third frequency which is at the frequency of the difference of the frequency of the two sources which is called the “Beat Frequency.”  In this case the beat frequency is 3 Hz.

Beat Frequency (Hz) = Abs(F1 (Hz) – F2 (Hz))

“Abs” indicates that the resulting number has no sign.  If the two source frequencies are selected so that the result is a negative number, the minus sign is discarded as only the difference between the two frequencies is important.  The following illustration shows what happens if the frequency difference between the two sound sources shown above is doubled.

The third frequency resulting from the combination of two sources operating at different frequencies is, although “fabricated,” very real in terms of its impact.   It has the same effect as a third sound source operating at the “Beat” frequency.

In music (which is a good model for a lot of ideas about sound), it is the beat frequency that produces the effect commonly called “harmony.”  When the sound of two singers or instruments singing or playing different frequencies or “notes” at the same time combine to produce a pleasing result it is usually because the third frequency results in a “chord” of notes.  Without going into a lot of detail, “chords” are combinations of musical notes that produce a sound that the human ear finds pleasing.  Interestingly, different people and cultures have different perceptions of what sound combinations are pleasing.  That is why some combinations of notes are musical to some people but are just noise (or worse) to others.

As you can imagine, things get even more complicated when more than two frequencies are combined.  The result can be very complex as both primary and beat frequencies interact and, again, can be either harmonious or discordant.  Musicians and composers are very sensitive to the interactions of tones.  They use them in endless combinations in conjuction with rhythms to produce an unlimited range of musical effects.

Just as musicians have to be aware of the interactions of frequencies, so must engineers who utilize sound in other ways including ultrasonics.  In some cases, although the primary frequencies produce desired effects, the third or beat frequency may result in effects that are less than desirable.  We will discuss these effects in more detail when we discuss resonance and other topics under the heading of ultrasound.

–  FJF  –