Acoustics II - Wave Theory

When we talk about acoustics, a minimal understanding of wave theory is indispensable. It might seem a bit intimidating at first, but it's quite simple once we understand the concept.

In the previous post, we unraveled what sound is: an energy wave that travels through a medium. Now, let's take the next step and learn the "language" of this wave. Just as we describe an object by its height, weight, and color, we describe a sound wave by its fundamental properties. Mastering these four concepts—frequency, period, wavelength, and amplitude—is what allows us to make precise technical decisions in the studio, from microphone placement to the acoustic treatment of a room.

The 4 Properties of the Sound Wave:

• Frequency (Hz): Defines the pitch of the sound (from low/bass to high/treble). It is measured in cycles per second.

• Period (T): Defines the time it takes for a wave to complete one cycle. It is the inverse of frequency.

• Wavelength (λ): Defines the physical size of the wave in space. Low-frequency sounds have long wavelengths; high-frequency sounds have short ones.

• Amplitude: Defines the intensity of the wave. It is directly related to the volume or "loudness" of the sound.

1. Frequency (f): The Pitch of the Sound

Frequency is perhaps the most intuitive property of the sound wave. It tells us how many complete cycles of compression and rarefaction occur in one second. The unit of measurement for frequency is the Hertz (Hz).

• Relation to Music: Frequency is directly linked to the pitch of a note.

  • Low Frequencies (Bass): Fewer cycles per second. Ex: The sound of a double bass.

  • High Frequencies (Treble): Many cycles per second. Ex: The sound of a piccolo.

• Human Perception: The healthy human ear is capable of perceiving frequencies ranging approximately from 20 Hz to 20,000 Hz (or 20 kHz).

2. Period (T): The Time of a Cycle

The period is the partner concept to frequency. While frequency counts how many cycles occur in one second, the period measures how much time (in seconds) it takes for a single cycle to be completed.

The relationship between them is purely mathematical and inverse:

• Period (T) = 1 / Frequency (f)

• Frequency (f) = 1 / Period (T)

This means that high-frequency waves have a very short period, and low-frequency waves have a long period.

3. Wavelength (λ): The Physical Size of Sound

This is where things start to get very interesting for room acoustics. The wavelength (represented by the Greek letter lambda, λ) is the physical distance a sound wave travels in space to complete one cycle.

The wavelength depends on two things: the speed of sound in the medium and its frequency. The formula is:

• Wavelength (λ) = Speed of Sound (v) / Frequency (f)

Crucial Practical Impreplication:

• A high-pitched sound of 10,000 Hz has a wavelength of only 3.43 centimeters.

• A low-pitched sound of 40 Hz has an impressive wavelength of 8.5 meters.

This is why low frequencies are so difficult to control in small rooms. An 8.5-meter wave simply doesn't "fit" properly in a bedroom, which generates standing waves and an irregular bass response. It is also why porous absorption panels don't work very well for low frequencies.

4. Amplitude: The Intensity of Sound

Amplitude refers to the maximum intensity or "pressure" that a sound wave reaches relative to its resting point. In simple terms, amplitude is directly related to the volume or loudness of a sound.

• Higher Amplitude: More displacement of air particles, higher sound pressure, louder sound.

• Lower Amplitude: Less displacement, lower sound pressure, quieter sound.

It is important not to confuse the physical measurement of amplitude (usually measured in Decibels, dB) with perceived loudness measurements like LUFS, which are more complex and take into account the duration and frequency of the sound. Amplitude is the "raw" measure of the wave's energy.

The Speed of Sound (v): The Influence of the Medium

The speed of sound is not a universal constant. It depends on the medium in which the wave is traveling. In air, at a temperature of 20°C (68°F), the speed of sound is approximately 343 meters per second (1125 feet per second).

The most important factor that alters this speed is the density of the medium—the denser, the faster:

• Sound travels faster in liquids than in gases.

• Sound travels even faster in solids than in liquids.

This is why you can hear an approaching train by putting your ear to the rail long before you can hear it through the air.

Conclusion: Uniting Theory and Practice

Understanding these properties transforms the way you interact with audio:

• Understanding Wavelength helps you decide on microphone placement and understand why acoustic treatment is so crucial for low frequencies.

• Knowing the Period and Speed of Sound is the first step to understanding phase phenomena and calculating delay times.

Now that we have this foundation, we are ready, in the next post, to explore how these waves interact with each other, diving into the concepts of phase, polarity, and the dreaded comb filter.

Until then!