Sine waves and square waves. They sound different don't they? The square wave is
bright and maybe a little harsh where the sine wave is rounded and mellow. So
you'd think you could easily tell the difference between a sine wave and a
square wave. Well, as I'll show you in this video, that might not always be so.
Here's a preview...
Well that was obvious. The sine wave and the square wave sound completely
different. I'm going to show you how things can change as the frequency gets
higher. Don't forget to subscribe and click the bell to get notified every
time I upload a new video. First things first...
How did I set this up? Well firstly I generated the waveforms digitally so
I've got perfect square waves and perfect sine waves inside my digital
audio workstation software but then they go through the output of my audio
interface to the oscilloscope so the oscilloscope is showing what comes out
of the audio interface. So this accounts for some things you'll see on the screen
of the oscilloscope. Firstly the tops and bottoms of the square waves - You'll
notice that they're slanted. The reason for this is because of the high-pass
filter in the output of the audio interface. That's to get rid of
frequencies below the normal human audio range which aren't any use to anybody.
And secondly you'll see some ringing just after the transitions from low to
high and high to low. This is caused by the filter - The low-pass filter in the
digital-to-analog converter which gets rid of frequencies which are above the
range of human hearing, which once again aren't of any use to us. I could have
used a function generator to generate a really clean square wave which would
look great on the oscilloscope. The problem with this however is that's not
what you're going to hear. You're going to hear the signals coming from your
audio interface or the audio output of your computer. So therefore you're going
to hear these slanted tops and bottoms and the ringing as well. So what you hear
corresponds very well to what you see on the screen. If I'd used a function
generator that wouldn't be the case. Maybe I'll use a function generator in a
future video. We'll see how it goes. Leave a comment if you'd like me to do that.
Okay let's dive into the video. I am going to
demonstrate the difference in sound texture between a square wave and a sine
wave and show how they become subjectively increasingly similar at
higher frequencies. I'll play a signal that alternates between square wave and
sine wave starting at 100 hertz. You will hear the difference clearly.
As you can hear, the square wave has a very much brighter and harsher tone
compared to the sine wave which is very smooth. The levels have been set to the
same RMS values so that both waveforms should be subjectively equally loud. Now
I will increase the frequency to 1000 hertz or 1 kilohertz. As I continue to
increase the frequency I will adjust the timebase control of the oscilloscope
so that you can see the shapes of the waveforms clearly.
At 1 kilohertz the square wave and the sine wave still sound very different to
each other. I will increase the frequency in 1 kilohertz steps. 2 kilohertz.
3 kilohertz.
4 kilohertz.
At this point you will probably start to hear both waveforms as being very
similar apart from a small difference in level but I will explain in a moment.
Let's move more quickly through the frequency range. 6 kilohertz.
8 kilohertz.
10 kilohertz, 12 kilohertz,
At this point both waveforms sound pretty much identical. The reason for
this is that the brightness of the square wave is caused by its harmonics.
Where a sine wave only has one frequency component - its fundamental - the square
wave has the fundamental and harmonics at whole odd-number multiples of the
fundamental frequency. So in a 100 hertz square wave you hear frequency
components of 100 hertz, 300 hertz, 500 hertz, 700 hertz and so on all the way up
the frequency band. As you can see in this spectrogram. When we get to a
fundamental frequency of 4 kilohertz however the next frequency component,
which we call the third harmonic, is at 12 kilohertz. Many people can't hear
frequencies as high as this. At a fundamental frequency of 8 kilohertz the
third harmonic is at 24 kilohertz, which hardly anyone is capable of hearing. It
is also worth saying that digital audio sampled at 44.1 kilohertz, which is
common, can't reproduce 24 kilohertz either. A sampling rate of 96 kilohertz
was used to make the original recordings here to show on the oscilloscope to
allow a margin of safety. So as the frequency increases the harmonics of the
square wave become inaudible leaving only the fundamental. So at a high enough
frequency it sounds exactly the same as a sine wave. Finally let me explain the
slight differences in level. Well if the harmonic components of the square wave
are being lost at very high frequencies, the overall level will therefore be a
little lower. You might also notice some ringing in the square wave signal. This
is probably being created by filtering in the digital-to-analog converter. The
ringing frequency is around 46 kilohertz so it is well above the audio band.
The oscilloscope, by the way, is specified up to 20 *megahertz* so we can expect it
to be completely clean in the audio band. In summary, at increasing frequencies a
square wave begins to sound more and more like a sine wave. So there you have
it. A square wave sounds pretty much like a sine wave at higher frequencies. It's
all part of the fun of audio and I love it. Don't forget to subscribe and click
the bell to be notified every time I upload a new video, and of course there
are other Audio Masterclass videos to enjoy. I'm David Mellor, Course Director of
Audio Masterclass. Come and visit us at AudioMasterclass.com and take a look
at our range of courses in Music Production and Sound Engineering, all
online. Thank you for listening.