What is rarefaction?
And what about amplitude?
Hm, I’m not so sure
—A haiku about why you are reading this article.

When we listen to music, we’re primarily left with our thoughts, impressions, and emotions that transcend technical explanations. Understanding the physical reality that such a sublime force occupies, however, can offer a seismic shift in perspective. Whatever your reason is for digging deeper, you know why you’re here, and that’s what matters: welcome to the beginner’s guide to sound waves!

If you’re new to acoustics, or just peripherally familiar with it, you are in the right place. Now let’s dissect some waves.

What Makes a Sound Wave? Rarefaction and Compression

Everything in the universe can be categorized as either matter, or energy. A sound wave is an energy wave. It can only be observed through its effects on matter; in most cases, air particles.

So what is a sound wave doing to air particles? It is compressing and rarifying them.

Compression refers to the phenomenon of air particles pushing together and increasing in density. Rarefaction is the opposite: air particles are spaced further apart and decrease in density. A sound wave is defined by its rapid and repeated compression and rarefaction of air particles, which we in turn perceive as a sound. The technical term for this back and forth is oscillation.

So what is a soundwave? Air particles oscillating between compressed and rarefied states; a pattern of modulated air pressure.

There is a somewhat paradoxical realization to be had here: a sound wave (energy) can only be defined by its relationship to what it is not (matter, air particles). Sound isn’t “made” out of particles, yet particles must be present in order for us to measure or perceive a sound. Pontificating on this isn't completely necessary to understanding the subject at hand - just something to think about.

Frequency

Finally, a term you probably recognize, right? High frequencies are high pitched, low frequencies are low pitched.

But let's take the word "frequency" literally - how frequently *something* is happening. When it comes to sound waves, frequency refers to how frequently the oscillation between compression and rarefaction is occurring.

The wavelength on the bottom is of a higher frequency than the wave above it. It oscillates, compressing and rarifying air particles more frequently.

The unit for measuring frequency is Hertz (Hz), which denotes cycles per second. In the context of sound waves, 1 Hertz represents one complete cycle of compression and rarefaction. A 20 Hertz wave rarifies and compresses air particles 20 times per second, while a 20 Kilohertz wave (1,000 Hertz = 1 kilohertz [kHz]) rarifies and compresses air particles 20,000 times per second.

By the way, the frequencies used in that example weren’t randomly selected: 20 Hz to 20 kHz constitutes the total range of human hearing.

But to sum it up, frequency indicates the rate at which a sound wave oscillates between rarefaction and compression. Frequency has an inverse relationship with wavelength, but we’ll come back around to that after we talk about amplitude.

Amplitude

While frequency measures the rate of compression and rarefaction, amplitude measures the intensity at which compression and rarefaction occurs. The unit we use for measuring amplitude is decibels (dB). Sound waves with high amplitudes compress and rarefy air particles with a greater intensity than sound waves with low amplitudes.

The vertical dotted lines represent amplitude measurements. The point of greatest amplitude in a wave cycle is called the peak.

It’s tempting to say that that amplitude is completely synonymous with loudness. To some extent, this is true: we can generalize and say that we perceive sounds with high amplitudes as being loud. But there’s a little extra nuance that distinguishes loudness from amplitude.

Loudness is a subjective quality concerned with how we perceive sound. Amplitude is an objective quality concerned with how we measure sound.

A few examples to illustrate the difference between loudness and amplitude:

• A sound wave with an amplitude of 100 dB will be louder for a dog than for a human.
• Humans are particularly sensitive to sounds in the 4 kHz region, thus we perceive a 4kHz sound wave as being louder than a 30 Hz sound wave even if both are played at the same amplitude.
• Sounds with amplitudes below 20 dB are generally imperceptible to humans. A wave with an amplitude of 19 dB is just as loud as a wave at 0 dB - that is, completely silent.

So, amplitude is not loudness, even though the two have a close relationship with one another. Amplitude is specifically the intensity at which a sound wave moves air particles.

Wavelength

The wavelength of a sound wave is the physical distance that it takes for a wave to complete one cycle of rarefaction and compression. Generally, wavelength measurements are taken by measuring the distance between the peaks of wave cycles, as they are an easily identifiable reference point for measurements. A peak is simply the point of greatest amplitude in a wave cycle.

As I mentioned earlier, frequency and wavelength have a directly inverse relationship with one another. High frequencies have short wavelengths, while low frequencies have long wavelengths. Why is this?

High frequencies oscillate more frequently than low frequencies, and in turn produce wave cycles that are shorter in physical length. Once again, a visual will make this a bit easier to understand:

The high frequency wave on the bottom exhibits a shorter wavelength than the lower frequency wave above it as it oscillates more frequently.

The Interplay of Frequency, Amplitude, and Wavelength

Let’s go over all the concepts we discussed with a relatable example:

Have you ever been to a concert and noticed that you can only hear lower frequencies when you’re standing outside of the venue? This has everything to do with the interplay of frequency, wavelength, and amplitude.

With every compression-rarefaction cycle that a sound wave completes, it loses a portion of its energy and decreases in amplitude - a technical way of saying that sound waves lose intensity over distances. So, you’re in the parking lot, let’s say 1,000 meters away from the speakers in the concert venue. The guitar player is soloing, playing high notes in the 2 kHz to 4 kHz range. The bassist is laying down a bass line with notes in the 50 Hz to 200 Hz range. By the time the sound waves reach your ears, the guitarist’s 4 kHz notes have oscillated 80x more frequently than the bassist’s 50 Hz notes. The guitarist’s high frequency waves, with their shorter and more frequent oscillations, have lost quite a bit more amplitude than the sound waves emanating from the bassist by the time you’re hearing them.

• Higher frequencies = smaller wavelengths = greater number of oscillations over 1000 meters = more rapid loss of amplitude over 1000 meters
• Lower frequencies = larger wavelengths = fewer number of oscillations over 1000 meters = less rapid loss of amplitude over 1000 meters

Did you like that? We can get even more technical with it.

Sound waves travel at a speed of 343 meters per second. If you’re standing 1,000 meters away from the sound source, sound waves have been traveling for 2.9 seconds before reaching your ears - let’s say 3 seconds so we can work with a nice whole number. How many times has a 50 Hz wave oscillated in 3 seconds versus a 4 kHz wave?

• 50 Hz x 3 seconds = 150 oscillations/cycles
• 4,000 Hz x 3 seconds = 12,000 oscillations/cycles

12,000 divided 150 is 80 - would you look at that, the math checks out. Just a different approach to the same conclusion: lower frequencies can travel farther than high frequencies due to their infrequent oscillations and longer wavelengths.

Just Give Me the TLDR

• A sound wave is an energy wave that modulates air pressure by compressing and rarifying air particles.
• The frequency of a sound wave denotes how many times the wave oscillates between compressing and rarifying air particles per second.
• The amplitude of a sound wave is the intensity at which it rarifies and compresses air particles.
• The wavelength of a sound wave is the measurable, physical length that it takes for a sound wave to complete one oscillation.
• Sound waves lose amplitude with every oscillation they complete.
• High frequency waves lose more amplitude over distances than low frequency waves due to their more frequent oscillations and shorter wavelengths.

This article is only scratching the surface when it comes to the physics of sound waves, but the concepts discussed here lay a foundation for a more intricate understanding of the subject. Whether you arrived here because you’re getting started on a longer journey in acoustic sciences, or you’re just a curious music listener who got more than they asked for, you’re now thinking in a way that can hopefully make your everyday auditory experiences all the more rewarding.