Oscillations, Waves, and Acoustics Vocabulary

Vocabulary flashcards covering oscillatory motion, simple harmonic motion, wave mechanics, and architectural acoustics based on lecture notes.

Oscillatory Motion

Motion that occurs when a body is subjected to a force that varies in time.

Inertia

The property that causes an oscillating body to overshoot its equilibrium position.

Simple Harmonic Motion (SHM)

Oscillatory motion where the restoring force is directly proportional to the displacement from equilibrium.

Hooke's Law

The mathematical relationship representing restoring force $F = -kx$, where the negative sign indicates the force is directed opposite to the displacement.

Standard Differential Equation for SHM

$$\frac{d^2x}{dt^2} + \omega^2 x = 0$$

Displacement Equation in SHM

$x = A \sin(\omega t + \phi)$, where $A$ represents the amplitude of the oscillation.

Velocity in SHM

$v = \frac{dx}{dt} = \omega A \cos(\omega t + \phi)$, reaching its greatest magnitude at the midpoint (equilibrium position).

Acceleration in SHM

$$a = -\omega^2 x$$

Potential Energy in SHM

$$U = \frac{1}{2}kx^2$$

Total Energy in SHM

$$E = \frac{1}{2}kA^2$$

Free Oscillations

Oscillations that result from a single initial deviation and are maintained solely by internal restoring forces.

Natural Frequency

The frequency with which a pendulum or physical system oscillates freely on its own.

Damping

The phenomenon of decay in the amplitude of oscillations due to energy dissipation, governed by frictional force $F' = -bv$.

Underdamped System

A system characterized by weak damping under the condition $\frac{\gamma}{2m} < \omega_0$.

Critical Damping

A state in a mechanical system where it returns to equilibrium as fast as possible without overshooting or oscillating.

Forced Oscillations

Oscillations produced when an external periodic force is applied to a body.

Resonance

The dramatic increase in amplitude when the driving frequency is near the natural frequency of the system.

Wave

A disturbance that travels through a medium, transporting energy without transporting matter.

Longitudinal Waves

Waves in which particles vibrate parallel to the direction of propagation.

Transverse Waves

Waves in which particles vibrate perpendicular to the direction of propagation.

Acoustics

The branch of physics dealing with the origin, propagation, and auditory sensation of sound.

Infrasonic Waves

Sound waves with frequencies below $20\,\text{Hz}$.

Ultrasonic Waves

Sound waves with frequencies above $20\,\text{kHz}$.

Pitch

The subjective sensation of sound related to frequency that allows us to distinguish between a shrill and a flat note.

Timbre (Quality)

The characteristic that enables a listener to distinguish between notes of the same pitch and loudness played on different instruments.

Weber-Fechner Law

Law stating that loudness $L$ is proportional to the logarithm of the intensity stimulus $I$ ($L = K \log(I)$).

Threshold of Audibility

The standard zero intensity level at $1\,\text{kHz}$, defined as $10^{-12}\,\text{W/m}^2$.

Sound Intensity Level (IL)

Decibel level calculated as $IL = 10 \log_{10}\left(\frac{I}{I_0}\right)$.

Echo

A repetition of sound produced when reflected waves reach the ear at least $100\,\text{ms}$ after the original sound, requiring a minimum obstacle distance of $17\,\text{m}$.

Reverberation

The prolongation of sound in an enclosed space due to multiple reflections after the source has stopped.

Reverberation Time

The time required for sound intensity to fall to one-millionth ($10^{-6}$) of its original value (a $60\,\text{dB}$ drop).

Sabine's Formula

$T = \frac{0.161V}{A}$, where $V$ is volume and $A$ is total sound absorption.

Sabin

The unit of sound absorption, named after Wallace Sabine.

Absorption Coefficient (\alpha)

Ratio calculated as $\alpha = \frac{\text{Sound energy absorbed by the surface}}{\text{Total sound energy incident on the surface}}$.

Sound Foci

An acoustical defect caused by reflecting concave surfaces that concentrate sound at specific points.

Dead Spots

Points in an auditorium where there is a deficiency of reflected sound due to focusing elsewhere or interference.