# Would a square wave look like a sine passed through a material?

• arianna1012

#### arianna1012

Sorry for the wording of the topic- I couldn't figure out how to make it fit.

If I passed a hypothetical square wave through a material- be it wood, glass, cotton, etc.- would it change to look more like a sine wave?

Sorry for the wording of the topic- I couldn't figure out how to make it fit.

If I passed a hypothetical square wave through a material- be it wood, glass, cotton, etc.- would it change to look more like a sine wave?

It's not clear what type of wave you're talking about. Is it a sound wave?

If you think about what the transmission of a square wave actually involves, then it should be easy to see that matter can't have the response required to maintain that shape.

Another way to look at this, is a square wave as a superposition of waves of different frequencies. Most media preferentially filter out high frequencies. So yes, in general the low frequency components would be transmitted, which would leave something that tends towards a sinusoid from your initial square wave.

Exceptions to this would be media that act as high-pass filters, rather than low-pass filters. Again, the resultant wave wouldn't resemble a square wave, more like a sinusoid of higher frequency.

Effectively to maintain a square wave, you need to be able to transmit all frequencies equally.

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The answer is a qualified yes, if you are talking about sound waves.
A square wave can be regarded as a sum of infinite sine waves. If that is new to you, you really should read up on Fourier series. If you don't understand Fourier series, then you won't be able to understand the reasoning.

Usually, high frequency sine waves are damped more than low frequency sine waves, but of course this depends on the shape and substance of the material. If the material resonates with the sound wave, then the output will be different. If you remove the high frequency parts of the square wave, the step changes will become rounded off. The pure sine wave has only one frequency. If all the higher frequencies are removed, then you end up with a pure sine wave, but generally the material will only partially attenuate the higher frequencies.

Yes, I was talking about sound waves. Sorry that I didn't clarify that.

You may imagine applying a sine wave, say a steady tone, to a speaker. The speaker coil vibrates in and out, driven by the smoothly varying current.

Now, imagine applying a square wave to that same speaker. When the drive signal switches from "zero" up to "maximum" almost instantaneously, how fast can that speaker coil respond? Clearly it needs some finite amount of time to reach that maximum. The result is the speaker cannot reproduce the square wave. It physically cannot respond to a change in drive current fast enough.

The answer, as is often the case, is "it depends on the frequency response of the material".

If you think of a square wave in terms of it Fourier series, it is (roughly) the sum of infinite odd sine wave harmonics of decreasing amplitudes (1* (fundamental) + 1/3(third harmonic) + 1/5 (fifth harmonic) ... ). To the extent that the material you pass the squarewave through attenuates the high frequencies, the waveform changes to look more like its fundamental. To the extent the material attenuates the low frequencies, the more it looks like high frequency ringing.

Here is an example of how to make a square wave from sinewaves.
http://www.mathworks.com/products/m.../products/demos/shipping/matlab/xfourier.html

Also, wolfram has several neat demos if you download the cdf player.

Edit --- here is a perfect demo. You can remove low or high components and see what it does. It seems to be a safe app. http://www.falstad.com/fourier/

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