Introduction to Waveforms

In previous posts we discussed some basic properties of sound, how it's converted or transduced to an analog audio signal and then converted back to sound again. Now we're going to introduce some graphic images called waveforms. You're going to see waveforms everywhere as your studies in audio progress so let's make sure we have a basic understanding of what they represent.

Obviously we can't see sound pressure waves in the air but we do have tools that can measure them. From these measurements we can produce graphical representations of waveforms that are incredibly useful for understanding a sound wave's behavior. 

The image below illustrates how as a tuning fork vibrates it causes the air pressure around it to change. The darker area represents a compression, or increase in air pressure, while the lighter area represents a rarefaction, or decrease in air pressure. The compressions and rarefactions of air pressure alternate at the same rate, or frequency of the vibration of the tuning fork. When these changes in air pressure hit your ear they cause your eardrum to move back and forth at the same frequency. Your brain then interprets the vibrations of your eardrum as sound.

The waveform drawing (in red) describes the behavior of the sound pressure wave. The rising of the line depicts a compression while the falling line depicts a rarefaction. 

NOTE: this image is simplified for clarity. A sound wave would actually radiate outwards 360 degrees in all directions from the tuning fork.

If we cut the tuning fork in half it would vibrate twice as fast. This creates a sound wave that also doubles in frequency resulting in a pitch difference that we call an octave. 

To illustrate this the waveform graphic also doubles in frequency.

What if we were to hit the tuning fork with half the intensity that we had previously? It would vibrate at the same frequency and we would hear the same pitch. But since the fork is pushing against the air at half the intensity the resulting sound wave would have half the amplitude (we hear this as loudness). Notice how this is represented in the waveform drawing.

So now we should know that:

• The horizontal distance between cycles of the waveform indicate frequency 
• Differences in vertical height indicate changes in loudness or amplitude

Got the idea? If you're still not sure check out a great (and simple) video on the basics of sound by @MoogFoundation here.

The waveforms we've been discussing so far describe the behavior of sound pressure waves in the air. But in audio you're also going to run across (potentially) identical waveforms that are describing the properties of analog audio in an electrical circuit. What happens when you plug a microphone into a amplifier? What's being transmitted down the mic cable? Air pressure?

We know that sound waves are changes in air pressure.  

You've all heard the term voltage before. It's often described as an electrical pressure (trust me). 

A microphone converts the frequency and amplitude of a sound pressure wave to an electrical pressure of a proportional frequency and amplitude. This electric signal is what we call analog audio.

Finally it needs to be said that all of the waveforms illustrated here are sine waves. They're unique in that they only vibrate at a single fundamental frequency. Most musical sounds that you hear in the real world consist of multiple sine waves vibrating at mathematically related frequencies called harmonics. These multiple harmonics combine together to form complex waves with their own unique tonal character. Harmonics are why my voice doesn't sound like your voice and my grand piano doesn't sound like your kazoo. Read a little more about harmonics here and let me know if you have any questions, really!

The next post will cover a "bit" about binary code. After that we'll discuss analog to digital conversion and how these bits correlate to the digital audio parameters you set up in your DAW.  

Thanks for reading.

Karl Wenninger is an audio engineer, synthesist/sound designer, composer, guitarist and DIY audio electronics enthusiast. As an adjunct professor he has taught Pro Tools at The New School for Jazz and Contemporary Music, Computer Music at York College and Audio Post-Production for the Media Arts Program at NJCU. He was an program administrator and associate professor at the former Digital Media Arts program at Touro College in New York City for over a decade.