# Wave Interference and Beats

1. Apr 2, 2012

### austinv

I'm studying wave interference and I have a few questions regarding it that I can't quite figure out:

1.) I was once taught that for waves to interfere, they have to be of the same frequency, but then how can beat interference occur? What are the actual requirements for interference?

2.) As far as I know, for us to perceive beats, the difference between the frequency of the two waves can't be more than about 40hz, but then how is it possible to hear the beats when tuning a guitar? The two E strings on a guitar are one octave apart, right, which means one has double the frequency of the other, which is certainly more than 40hz?

3.) When two sound waves with slightly different frequencies interfere to create a beat, the "frequency" of the resulting wave is said to be the difference in frequency between the two waves that interfered; so wave A minus wave B. But that "frequency" is really variations in the loudness of a new wave with some other frequency. But what is that frequency, is it wave A's frequency plus wave B's frequency?

4.) Can the phenomenon of beat interference occur for light as well as sound? If it can, then why don't we see it?

Thanks so much!

This is such a great community and I thank all of you who contribute to it and help students like me.

2. Apr 3, 2012

### Exnihiloest

Interference is just two waves that add (vectorially, so they can cancel each other).
If the frequency is the same, the interference is only in space. So there are places where the waves cancel each other, or add constructively elsewhere.
If the frequency is not the same, the waves "beat" in time, depending also on the location in space. This means that the conditions for destructive or constructive interferences are time (and space) dependent.

I think there is a possible confusion. When waves interfere, there are never new frequencies. New frequencies appears only with a product of signals, not a simple sum, i.e. when a signal modulates another one. This implies either a nonlinear medium of propagation or a nonlinear "receiver" which creates the new frequencies that didn't exist in the media.
The ear is not linear (it is linear in dB, the sensation being proportional to the square of the excitation of sensory cells), so you can hear beats although there is no objective sound vibration at the beat frequency, what can be confirmed by a Fourier transform of the signal from a microphone.
Now from the "viewpoint" of the ear, there are physiological phenomena to be taken into account. They are not trivial, the brain plays a considerable role in the treatment. I guess that the ear is more sensitive to the difference of frequencies than to the sum or higher harmonics. It is no more a question of physics.

Generally there are both, and even others higher, depending on the nonlinearities and only if there is nonlinearities. For sounds in air, the medium is linear, there is no new waves. The beat you hear is an artifact coming from the way that your audition sense and your brain interpret the two real sounds of near frequencies.

It occurs for absolutely all kinds of waves.

3. Apr 3, 2012

### nasu

You don't hear beats between the two E strings, do you?
When you use beats to tune the guitar you use on one string as reference (tuned by tuning fork or other method). Then you push the second string against the appropriate fret so that is should give the same note as the reference string if it were tuned properly. If it is slightly off, you hear the beats. You change the tension until you don't hear the beats.
At least this is the tuning method that I know of.
If you pluck two free strings at the same time you don't hear beats. Maybe a chord.