Acoustics: Frequency, Amplitude, and Sound Perception

• Sound results from the vibration of matter, creating waves that move through a medium, typically air.
• The human ear detects sound waves ranging from 20Hz to 20kHz, converting them into electrical signals.
• Sound is characterized by frequency, amplitude, and timbre.
• Frequency is the number of cycles per second the sound wave completes, measured in Hertz (Hz).
• Amplitude is the size of the wave, determining loudness.
• Timbre is the sound's quality, influenced by overtones and other factors.

Frequency vs Amplitude

• The two key aspects of sound are frequency and amplitude.
• Frequency relates to pitch (high or low), measured in Hertz (Hz).
• Amplitude relates to volume or loudness, measured in Decibels (dB).
• Frequency and amplitude are independent parameters.

Pitch

• Pitch is the perceptual attribute of sound related to a sound wave's frequency.
• It is the subjective sensation of how high or low a sound is.
• Higher frequencies are perceived as higher pitches, and lower frequencies are perceived as lower pitches.

Perceiving Frequency as Pitch

• Humans perceive frequency as pitch due to how the auditory system processes sound.
• Sound waves enter the ear, travel down the ear canal, and vibrate the eardrum.
• Vibrations transmit through the middle ear to the cochlea, a spiral-shaped organ in the inner ear.
• The cochlea contains tiny hair cells that convert sound vibrations into electrical signals sent to the brain.
• Hair cells along the cochlea respond to different frequencies of sound.
• When a sound wave with a particular frequency enters the cochlea, the tuned hair cells respond.
• The brain interprets the pattern of activity across these hair cells as a particular pitch.
• The perception of pitch results from the auditory system processing different frequencies.

Longitudinal Mechanical Waves

• A longitudinal wave is when the particles' motion in the medium is in the same direction as the wave's propagation.
• A sound wave is an example of a longitudinal mechanical wave.
• Air molecules vibrate back and forth in the same direction as the propagating sound wave.
• This process creates compressions and rarefactions traveling through the medium.

Simple Harmonic Motion

• A system that vibrates at a constant frequency, regardless of amplitude, exhibits simple harmonic motion.
• Musical instruments need to exhibit this behavior to be tuned.
• Sound waves exemplify simple harmonic motion, a type of periodic motion.
• Restoring force is proportional to the displacement from the equilibrium position and directed towards it.
• Air molecules oscillate around their equilibrium due to pressure variations from vibrating objects, such as tuning forks or vocal cords.
• Oscillation follows the principles of simple harmonic motion, with the restoring force proportional to the displacement from equilibrium.
• Sound waves can be mathematically described as sine waves, the most basic form of simple harmonic motion.

Concept of Phase and Sound Waves

• Phase refers to the timing relationship between different sound waves.
• This is especially relevant in multi-microphone or multi-track recordings.
• Phase Shift occurs when sound waves are out of sync, causing alignment that either cancels or reinforces.
• Constructive versus Destructive Interference are ways sound waves can interact depending on their phase relationship.
• Managing phase is vital for audio clarity and balance.
• It can take time for audio engineers to discern phase changes.
• Phase coherence for mic placement ensures clear and accurate sound capture.
• It also prevents phase cancellation, and preserves audio clarity.
• Correct phase alignment in mixing ensures clarity and fullness.
• Phase issues can cause muddiness or cancellation.

Common Phase Problems

• Out-of-Phase Mic Placement occurs when multiple microphones or tracks pick up the same sound, which can cause phase issues.

Wave Addition

• Two sine waves of the same frequency that start at the same time are "in-phase". The combined wave has the same frequency, but double the amplitude, and are constructively reinforced.
• Conversely, if one wave is delayed by half a cycle, they will destructively combine, as they are out of phase.
• They will fully cancel each other out ONLY if they are of equal amplitude.
• In situations where two waves are 1/4 of a cycle out of phase, they combine to create a completely new wave

Dispersion

• When two different frequencies play at the same time a complex combined wave will form
• High frequencies disperse faster than low frequencies due to shorter wavelengths.
• Sound waves propagating through a medium cause particles to vibrate and transfer energy.
• As a wave travels, particles absorb and scatter some of its energy.
• This scattering causes the wave to spread out and weaken, known as dispersion.
• The amount of dispersion depends on wavelength impacting higher frequencies more. Shorter wavelengths are more susceptible to scattering compared to the longer wavelengths of lower frequencies.

Temperature

• Higher temperatures generally result in faster sound transmission.
• Warm air molecules move faster, thus transmitting sound waves quickly.
• Cold air molecules move slower, causing sound to travel more slowly.
• Higher temperatures reduce air density, aiding sound wave propagation.
• This results in faster sound travel in warmer air.
• Temperature changes affect the speed of sound, and consequentially the wavelength.
• Higher temperatures lead to longer wavelengths.
• Frequency (pitch) remains unaffected by temperature changes.