Oscillation and Vibration

Oscillation

• Repetitive back-and-forth motion around a reference point

Vibration

• A specific physical form of oscillation
• Typically involves a mass moving around its equilibrium
• A fundamental source of sound when that equilibrium is disturbed

Simple Harmonic Motion (SHM)

Key Concepts

• Motion characterized by a restoring force proportional to displacement (Hooke’s Law)
• Described by a sinusoidal function (sine wave)
• Defined by amplitude, frequency (or period), and phase

Relevance

• SHM serves as the theoretical backbone of acoustics
• Sine waves are the purest form of sound and build more complex waves

Additional Interactive Visuals

• Interactive Mass-Spring Simulation
• Circular Motion → SHM Demonstrator
• Web SHM Visualizer

Complex Vibrations

Real-World Complexity

• Real acoustic signals are rarely pure sine waves
• Comprised of multiple SHMs summed together
• Complex waveforms define timbre and texture

Amplitude and the Signal Envelope

Amplitude

• Height from equilibrium to peak; correlates with loudness

Signal Envelope

• Temporal outline of amplitude changes
• Identified stages: Attack → Decay → Sustain → Release (ADSR)

Visual resource: Envelope in music – ADSR stages and their fine structure.

Period and Frequency

Period

• Time for one complete oscillation (T)

Frequency

• Number of cycles per second (Hz); frequency = 1 / period

Frequency and Period Conversion

Frequency (f)

• Number of cycles per second, measured in hertz (Hz)
• Formula: f = 1 / T
• Try it: SensorsONE frequency→period calculator

Period (T)

• Time for one complete cycle, measured in seconds
• Formula: T = 1 / f
• More examples: Omni Calculator – Frequency

Phase

Concept

• Describes the position within a cycle (degrees or radians)
• Two waves with same frequency and amplitude but different phase can behave differently together

Impact

• Asynchronous phase shifts may be imperceptible
• Simultaneous multi-source phase relationships affect loudness, timbre, and spatial cues

Logarithmic Scales in Acoustics

Why Logarithmic?

• Human perception of stimulus is proportional to logarithm of intensity (Fechner’s Law)
• Compresses wide dynamic ranges into manageable scales

Applications

• Express acoustic quantities (power, intensity, pressure) in decibels (dB)
• Aligns measurement scale with human hearing sensitivity

Common Sound Levels

Examples

• ~180 dB – Rocket launch (irreversible hearing loss)
• ~120 dB – Live rock band (pain threshold)
• ~60 dB – Normal conversation
• ~0 dB – Threshold of hearing

RMS Amplitude

Definition

• Root-Mean-Square (RMS) measures energy of oscillating signals
• Takes absolute values into account positive and negative deflections

Purpose

• More accurately correlates with perceived loudness than peak levels for sinusoidal and complex signals

Superposition and Interference

Superposition

• Multiple waves add algebraically to produce a complex resultant

Interference

• Constructive: waves amplify each other
• Destructive: waves cancel out
• Beats arise from near-frequency waves (fluctuating amplitude)