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. 

Sound Waves, Transducers and Analog Audio - Part II

In the previous post we discussed sound waves, transducers, alternating current and direct current. Then we looked at how a sound pressure wave is converted to an analog audio signal with a microphone. Here's a recap:

• A sound pressure wave is a vibration of air molecules
• A transducer converts one form of energy to another
• A microphone is a transducer that converts a sound pressure wave into an analog audio signal
• Analog audio refers to AC (alternating current) that is alternating (moving back and forth) at frequencies and amplitudes proportional to the sound wave in front of the mic

Got that? Let's move on

If you have a dynamic mic like a Shure SM58 put a finger across the three XLR pins on the back of it. Talk into the front. You won't feel a thing but trust me, there's a voltage there.

• A microphone outputs a very weak signal: sometimes as little as 2 millivolts (that's thousandths of a volt). This signal is not surprisingly called mic level
• The pro audio equipment that you're going to plug your mic into is designed to operate at an average of 1.23 volts. This average level for pro audio gear is referred to as line level

Just to give you some common reference points for voltage:

An AA battery cell has a potential of 1.5 volts. This can't physically hurt you.

The AC voltage from a household wall socket in the US averages about 117 volts. This can potentially hurt you so don't muck around with it.

Back to our analog audio signals:

• We know our microphone has a mic level output of about .002 volts 
• We need to boost the mic output up to around 1.23 volts line level before we can send it off for further processing or amplification

Let's do the math:

1.23/.002 = 615

To bring a microphone's output up to line level we're going to have to amplify it around 615 times. That's quite a lot! The circuit that's going to do this amplification for us is called a preamplifier.

If you've spent any time around audio engineers the subject of preamps or "pres" has probably come up. There are many different preamp designs by many different manufacturers. Heated debates often ensue regarding which preamp pairs best with which mic and in which application. I'm not going to get into those debates here but I will say that these circuits are very purposefully designed to sound different.

• Some preamps provide what's referred to as a "transparent" sound in that they don't change the overall tonal characteristics of a microphone
• Other preamps are popular among engineers for the exact opposite reason; they add their own tonal "color" to the signal

After the preamp boosts the mic signal to line level it's often sent off for further processing. This could involve adjustments to tonal qualities (equalization) or output levels. Note that at this stage our analog audio signals are still at line level.

After signal processing the line level output is sent to a power amplifier where it's boosted further. During this stage the signals are given enough power to physically push loudspeaker or headphone drivers back and forth.

Most of you are going to find this power amplification stage built into your active studio monitors. 

• An "active" device is capable of amplification
• A "passive" device is not (a passive speaker enclosure would require an external amplifier)

Like microphones, the drivers (speakers) in your monitors are also transducers. They convert analog audio signals to sound pressure waves.

• When the alternating current from the amplifier moves in one direction it pushes the driver out. When the current moves in the opposite direction it pulls the driver in
• The mechanical movements of the driver cause the air molecules around it to vibrate and create sound pressure waves in the air

To review let's take a look at a block diagram of the sound reproduction system we have described in these two articles:

• A microphone converts or transduces sound pressure waves to an analog audio (alternating current) signal of corresponding frequency and amplitude
• the weak output signal of a microphone is referred to as mic level
• A preamplifier boosts the mic output to a stronger level that pro audio gear requires to operate. 
• this is called line level 
• At this point signal processing such as EQ or adjustments to output levels can be applied
• After processing a power amplifier then boosts the line level signal to an amount that is capable of physically pushing a driver (speaker) back and forth 
• The mechanical motion of the driver transduces the electrical energy of the analog audio signal back to a sound pressure wave in the air

Got it?

If not let me know and we'll try to clear it up!

Next time we're going to talk a little bit about what those waveform graphics you keep seeing in all those textbooks really mean.

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. 

Sound Waves, Transducers and Analog Audio - Part I

We all understand that sound is made of vibrations in the air: when an object physically vibrates back and forth at repeating frequencies it causes the air molecules around it to vibrate at the same frequencies. These vibrations in the air create a sound wave that travels outward from the object in all directions. When the sound wave hits your ear it causes your eardrum to vibrate at the same frequencies. Your brain then interprets your eardrum's vibrations as sound.

The vibrating object, the sound wave and your eardrum are all vibrating at the same frequencies

A transducer converts one form of energy into another. In the example above we have two transducers:

• The vibrating object: its mechanical energy created the acoustical sound wave's energy in the air
• Your eardrum: the acoustical sound wave's energy caused it to send electrical impulses to your brain

If we want to convert a sound pressure wave in the air to an analog audio (electrical) signal we'll need another type of transducer. But to really understand how this works it will help if we learn a little about how electricity moves through a wire or circuit first. So let's talk about AC/DC. 

• AC stands for alternating current
• DC stands for direct current

Current refers to electricity moving or flowing through something. In a direct current (DC) circuit charges only move in one direction.

Batteries supply DC. If you were to connect the positive side of a battery to one terminal of a light bulb, and connect the second terminal of the bulb to the negative side of the battery, you would have created a simple circuit utilizing direct current.

Note: the diagram above illustrates what it known as "conventional current" and is used for simplicity. Electrons actually flow from - to +. Here's a link if you want to know more.

You could make another simple (but not very useful) circuit by connecting the terminals on the battery to the two terminals on a speaker. Because the direct current from the battery only moves in one direction the speaker cone would push outward as soon you closed the circuit. And the cone would remain that way until you disconnected it. If you don't believe me watch this guy do it on YouTube.

For our purposes we want the speaker cone to vibrate fast enough to create a sound wave. So sending DC to a speaker doesn't seem very useful. Good thing we have AC.

In a circuit that employs alternating current (AC) the current flows differently: instead of moving ahead in one direction it moves back and forth at a repetitive frequency. What else have we talked about in this article that does that? If you don't remember go read the first paragraph again. It's important that you see a correlation here!

So what if we want to convert a sound wave in the air to an electrical signal? Remember we said that a transducer converts one form of energy to another. The transducer we're going to use here is a microphone.  

Inside a microphone is a very sensitive diaphragm, sensitive like your eardrum. When the energy of a sound wave hits the diaphragm it begins to vibrate at the same frequencies. Get a cable and connect the mic to a sound system. What's being transmitted down the cable is an AC signal that is alternating, or vibrating back and forth, at the same frequencies of the sound wave in front of the mic. 

I just looked up the word "analogy" and got this: 

"a thing that is comparable to something else in significant respects"

The AC signal that's present on the mic output is analogous to the acoustical sound wave you put in front of the microphone. They both vibrate at the same frequencies. 

When you hear the term analog audio that's what it refers to: alternating current moving back and forth in a circuit at frequencies and amplitudes proportional to a sound pressure wave. 

So now we have:

A microphone by itself is pretty useless. So in the next installment we'll talk about preamplifiers, amplifiers and speakers.





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.