# Can a digital sound wave take any shape?

I'm studying the topic of sound waves in digital audio.

I have a basic understanding of the concepts of frequency, amplitude, samples, and how it all comes together to create a sound with a distinct pitch and 'tone' (timbre).

My question is this:

Can a sound wave take any shape? E.g. I know that there are sine waves (in the shape of a sine function), square waves, 'triangle' waves, etc. Can a wave take any shape and be heard in a distinct timbre?

Also, as a separate question: can two one sine waves in the same frequency sound different? Does 'sine wave' mean a very specific shape? Or can a 'sine wave' take many kinds of shapes?

A perfect sine wave can only be one shape as it is derived from geometry:

So it always sounds the same.

But yes, a wave can take any shape and this affects the timbre. An interesting point however, is that these movements all need to be reproduced by the speaker, which is possibly the weakest link in the chain. Consider how a speaker reproduces a perfect square wave?

According to theory, all complex sound waves can be decomposed into a set of sine waves, which are the most basic of wave shapes. Two sine waves of the same frequency will be identical except possibly for amplitude. That is, one may be louder than the other, but they're otherwise the same and can't be distinguished.

Can a digital sound wave take any shape? Now, there's no such thing as a digital sound wave. But most digital (16 bit wav 44.1kS/s, 24 bit wav 48kS/s, and higher quality) will get you VERY CLOSE to any reasonable shape. There will be some limitations, For example, very low amplitude sine waves will have noticeable quantization distortion. Also, frequencies past the Nyquist can't be represented, which may result in aliasing, depending on how the high frequency content got there.

A whole nother question is whether a real sound wav can have certain arbtrary shapes. For example, look at real world measurements of speakers attempting to produce square waves, for example these headphone measurements. I can confidently say that you will never see find a truly square sound wave in the real world.

The only shape a digital sound wave can not take is a perfect square wave (or impulse but its the same issue). This is a mathematical limitation caused by the electronics them selves. They simply need time to respond. Basically if you consider the sides of the square wave as perfectly vertical and the top as perfectly flat you will come to the realization that electronics simply can not change state that fast. Thus you actually end up with an almost instantaneous (yet measurable) ramp up, a top that looks like a diminishing sine wave, and an almost instantaneous ramp down. If you are curious about this read up on impulse responses or check this animation out http://upload.wikimedia.org/wikipedia/commons/f/f8/SquareWave.gif

As mentioned above any wave can be broken down to a series of sine waves thus, yes sound can take on any "shape"

• "The only shape a digital sound wave can't take"? Obviously, there are lots of shapes a band-limited wave can't have, and they needn't even have discontinuities. Even a triangle can't be done exactly! – leftaroundabout Oct 1 '14 at 16:33