# physical difference between A and B

We all know that when we say A it sounds different than when we say B. I was wondering what exactly can be the difference between saying A and B in terms of physics. I first thought that it may due to difference in the combination of frequencies. Then I realized I can say any alphabet in many different tones.

So what exactly in terms of physics is the difference between saying A and B ?

Interesting, I was just studying the Fourier decomposition of vowels for half an hour yesterday.

First, you must distinguish vowels and consonants. Words like "bee" (which is how we spell the letter "B") of course aren't uniform sounds. They start with a consonant, in this case one created by lips. Depending on the way how they're created, consonants are divided to many groups. See a table of consonants here.

In general, consonants are types of noise because they don't have a well-defined basic frequency. It means that the Fourier series for a consonant is composed pretty much of all sufficiently high frequencies. The color of the noise – whether higher frequencies tend to be more strongly represented than the lower one etc. – determines the type of the consonant.

There are consonants with a throat sound added, like L,M,N, which may be Fourier decomposed similarly to the vowels, and noise-based consonants such as B,D,G,V,Z which are the sound-equipped cousins of P,T,K,F,S, and so on, and so on.

The most monochromatic sounds are the vowels. They can be sung so they have a well-defined base frequency. Whether one gets U,O,A,E,I – or, in English, OO, AW, AH, EH, EE etc. – depends on how the mouth is opened. This modifies the shape of the resonance cavity and therefore the preferred additional frequencies that are excited by the action of the base frequency coming from the throat.

The presence of higher harmonics is essential for the difference between vowels. I recommend you to look at a page about it, for example this one:

http://hyperphysics.phy-astr.gsu.edu/hbase/sound/vowel.html

The vowel U (OO in English) has the lowest representation of the higher harmonics. It is the closest one to the harmonic sound and it's achieved by changing one's mouth into a passive tube through which the sound penetrates. On the other hand, A (AH) and I (EE) have a huge, important contribution of higher harmonics and when I say higher, I don't mean the 2nd or 3rd. The 20th harmonic etc. etc. are very important.

In fact, it's more accurate to talk about the absolute frequencies. The vowel A (AH) has lots of those higher harmonics that are close to 1,000 Hz (cycles per second) which are already suppressed in U (OO) and partly suppressed in O (AW). As you continue to go towards E (EH) and I (EE), the contribution from frequencies close to 3,000 Hz starts to increase.

These frequencies are calculable from the size of the mouth opened in the right way, from the length of the resonant cavity that becomes comparable to the wavelength of the sound waves that become important.

In principle, all vowels may be emulated by the Fourier expansion using just the base frequency (pressure goes like $\sin \omega t$) plus higher harmonics but the very harmonics including $\sin 20\omega t$ are still very important for the character of the vowel.

Phonetics is the portion of linguistics that studies how language sounds; the experts partially learn some physics although Fourier series aren't their primary tool. Still, to understand phonetics, one has to accept various basic things. I found out that native English speakers misunderstand phonetics because they don't really decompose the language into "pure sounds". Your representation of "B" as a sound analogous to "A" may be an extreme example because you may have meant "B" in the sense of "bee" which is clearly composed of two sounds, the consonant "B" and the vowel "EE".

But even when it comes to vowels only, English (and French and some other languages) is deliberately obscuring the reality as it pronounces many vowels in a variable way. For example, "my" is pronounced as "mai" where the vowel gradually changes from "AH" at the beginning to "EE" at the end. Some native English speakers don't even realize that this "Y" in "MY" isn't a single uniform vowel. There are many other examples, of course.

• Interesting answer. Does it really make sense to talk about the 20-th harmonics ? I though a human hear stops somewhere between (4-10)kHz, so do e still distinguish the 20-th harmonics ? Also, I contest your interpretation of French pronunciation (as I think any linguist would). In French, as in any continental european language to my knowledge, a vowel is always pronounced the same way, whatever its place in the word. French, German, Spanish, ... language nevertheless use accent. So there is a difference between a e and a é in French, but the e is always pronounced the same Jun 29, 2013 at 8:50
• ... way. Only English has diphthong vowel, which deeply complicated its pronunciation. In short, there is almost no rule of pronunciation in English (think about the word crisis or unimaginable where the two i are not pronounced the same way, despite being not associated to other letter, like it makes sense for pronounced for the two o). I always wonder why english has been chosen as an international language, it makes no sense to me regarding its not rational pronunciation. By the way, this has no more things to do with your interesting answer, sorry for this long comment. Jun 29, 2013 at 8:55
• Dear @Oaoa, human ears hear up to 20 kHz in average! Every human can hear 4 kHz. The ee-sounding vowels have important frequencies around 3-4 kHz but because they're primarily excited by the monochromatic sound from the throat, their frequency has to be a multiple of the base frequency, so they're very high harmonics. ... You may be right about French, I am no French speaker, but the way how French write the vowels etc. is surely complicated looking. Tableaux etc. Jun 29, 2013 at 13:16
• Thanks for the precisions. You're right for the 20kHz, it is usually believe to work... for babies ! Most of the people above 20 years saturates at (10-15)kHz. Whatever. You're also right for French, it's exactly the contrary than English: whereas French has several ways of writing the same sound (in your example: o, au, eau are the same sound, the same for é, et, ai ... despite phonetic distinguishes them, most French people do not) whereas English has several sounds for the same letter, especially the vowels... In short, French is (highly) redundant, English is not rational ! Thank again Jun 29, 2013 at 13:38
• @LubošMotl I am extremely grateful to you ,sir. But somethings still puzzle me which are relevant to this question. Lets consider a guitar string . As we go up and up over the fretboard we get different notes with the sound increasing in frequency. But after an octave ,we get the same note. What exactly are these notes in terms of physics? (Although A and B also denote notes but in the question I didn't mean them) .However, the tone of a guitar, i.e. the voice of the notes can be changed by different picking techniques or by using processors which do so by adjusting amp. of different harmnics Jul 3, 2013 at 12:28