# Are all sound waves periodic waves?

1. I am wondering what type of different sound waves there exists? Are all sound waves periodic waves, is there other types?

2. What does it mean when we put the word complex before a wave, like complex periodic wave?

I am new to physics and I've gotten confused about some terms and I would love it if someone could clarify them for me.

• An example of a sound wave that is not periodic : a sonar pulse. Used by submarines as well as bats (ultrasonic) for echolocating, the sonar pulse is a soliton sound wave, an isolated disturbance in the sound medium with no periodicity. Apr 2 '18 at 22:43

A function (a signal) is periodic in time when it repeats itself, when there is a period $T$ so that for all times $t$ it is valid that $f(t) = f(t + T).$

Only tones are periodic. For example a vowel has a period given by the movement of the vocal chords. Other sounds are not periodic: clicks, noise from waterfalls, the letter "s", etc. And even the sound from a bell is not really periodic: the frequencies do not have harmonic ratios. Same for a chord played on an instrument with equally tempered tuning.

"Complex" can mean different things. It may refer to the representation as complex functions like $e^{i\omega t}.$ Or it may be a wave that is not a sine function with just one frequency.

• Can you please clarify or tell me more about "Only tones are periodic." Apr 2 '18 at 19:44
• @HilulukAdde A tone has a pitch, a fundamental note with a certain frequency $f$. In general, the tone also contains harmonics (overtones) with frequencies $2f, 3f, ...,$ with amplitudes and phases that can be determined with Fourier integrals.
– user137289
Apr 2 '18 at 19:59
• Im getting a better understanding but could you perhaps give me an example or two of periodic waves that arent tones? Like something from nature? Thank you I really appreciate your help! Apr 2 '18 at 20:32
• @HilulukAdde There are no periodic waves that are not tones.
– user137289
Apr 2 '18 at 20:34