# Do two waves of different frequencies create a resultant wave of lower frequency?

In my results for testing background noise, i found that while strumming a guitar in:

a noisy area, the frequency picked up by the mic was 352 Hz

while in a quiet area, the frequency picked up by the mic was 358 Hz.

Is there any way I can explain these results and what I can attribute this to (like interference/beats/)

• Your answer lies partly in the answer to your previous question: physics.stackexchange.com/questions/202654/…. Beats aren't a permanent increase in frequency, instead frequency varies a periodically. For beats to occur the interference has to occur between waves of specified frquencies. 'Background noise' does not have a specific, fixed frequency, so would not be expected to cause beats. – Gert Aug 26 '15 at 22:49
• Is this experiment reproducible? If you go back and forth between noisy and quiet rooms do you always see a frequency difference? – DanielSank Aug 26 '15 at 23:27
• The answer, in your case, is no. The difference is most likely associated with slight changes to the physical properties of the guitar and its surroundings. One example: a change in temperature changes the length of the neck and therefore the tension in the string. – Chris Mueller Aug 27 '15 at 19:24
• Related question: math.stackexchange.com/q/1321811/3301 – John Alexiou Aug 27 '15 at 19:27
• If you add two or more periodic signals, then the frequency spectrum of the sum of the signals is just the sum of the frequency spectra of the individual signals. No new frequencies are introduced. If your microphone and other components of your frequency measuring instrument are all perfectly linear, then that is all that should happen. But, if there are any non-linearites in your measurement system, then new frequencies can appear in the signal. Audio engineers call that phenomenon harmonic distortion. – Solomon Slow Feb 22 '16 at 22:03

There are really two possibilities here:

• the guitar is going out of tune by 6Hz because of some environmental factor;
• the instrument measuring the frequency is being fooled by the background noise.

We can rule out the first of these with a high degree of certainty: a semitone at 352Hz is about 21Hz ($352\times (2^{1/12} - 1)$), so this would mean a short-term tuning change of significant fractions of a semitone: that doesn't happen to guitars except in quite serious circumstances such as being dropped or taken through a huge temperature change for instance. In such a case the whole guitar would be hopelessly out of tune with itself as well: you would know if this had happened.

So that leaves the second option: the pitch of the guitar has not changed but whatever is measuring it is being fooled by environmental noise. It isn't really possible to say much more about this without details of the device and its setup. However it certainly is the case that tuners for instruments can be mislead by 'dirty' signals in all sorts of ways: they're trying to do some phase-locked-loop thing to acquire the frequency and if the signal they are trying to lock to is cruddy they have a hard time.

One thing you said is that you strummed the guitar: if you mean this in its normal sense then you played a chord (possibly just the open strings). If you did that then there's really no hope for whatever is trying to acquire the frequency: it'll just pick up something random (probably not random, but nothing well-defined).

The difference in frequency is most likely due to the guitar going out of tune as a characteristic of background noise is that it does not have well-defined, constant frequencies, rather being a collection of all kinds of random frequencies thrown together.