Sound Waves and Sources
Basic Wave Phenomena
- What is a Wave? - a disturbance which travels through a medium
- Wave Motion in Space and Time - distinguishing between the time behavior and spatial behavior of waves
- Superposition of Two Waves - Interference, Standing Waves, and Beats
- Fourier Decomposition - building a wave shape from sines and cosines
- Phase changes upon reflection from hard, soft, and mixed boundaries
- Reflections from Impedance and the Standing Wave Ratio. - A sinusoidal wave train reflects from an impedance discontinuity. The resulting wave pattern defines the Standing Wave Ratio used to measure impedance.
- Refraction of Sound Waves - how temperature gradients make sound waves change direction
- The Doppler Effect - moving sound sources and sonic booms
Longitudinal Sound Waves
- Longitudinal and Transverse Waves - Particle Motion for Longitudinal, Transverse, Water and Rayleigh Surface Waves
- Phase Between Displacement, Velocity and Pressure for a Longitudinal Sine Wave - p and u are in phase for forward going waves, but have opposite phase for backward going waves.
- Phase Between Pressure and Particle Velocity for a Gaussian Pulse - p and u are in phase for forward going waves, but have opposite phase for backward going waves.
- Displacement vs Pressure -- Reflection from Boundaries - DRAFT page illustrating difference between the phase changes upon reflection for displacement pressure. (displacement inverts upon reflection from a rigid boundary while pressure reflects upright).
- How does sound reflect from the open end of a pipe? -- mass-spring model to illustrate how a longitudinal sound wave reflects from the open end of a pipe. New Animation => 2023 => (supported NYU Teaching Advancement Grant with Susie Levi)
- Standing Longitudinal Sound Waves. - Animating the relationship between particle motion and pressure in a standing longitudinal sound wave in a pipe.
Sound Sources, Radiation, and Scattering
- Sound Fields Radiated by Simple Sources - pressure sound fields produced by monopole, dipole, and quadrupole sources
- Directivity Patterns for an Acoustic Doublet (bipole) as a function of kd
- Sound Radiation from Cylindrical Radiators - particle motion and sound fields produced by vibrational modes of a cylinder
- Sound field radiated by a Tuning Fork - animations to accompany a paper published in the American Journal of Physics
- The Baffled Piston - approximation of the sound field radiated by a loudspeaker (This page is undergoing repair/updates)
- Partial Plane Wave Expansion -- expressing a plane wave in terms of spherical and cylindrical coordinates (for scattering problems).
- Scattering from Spheres and Cylinders - Scattering of a Plane Wave from Spheres (rigid and pressure-release) and Cylinders (rigid).
More Complicated Wave Phenomena
- Plane Waves and Evanescent Waves (Sound Radiation from Plates) - plane wave radiation of sound from bending waves in plates becomes evanescent when plate wave speed is slower than the fluid sound speed.
- Evanescent Modes in Waveguides - higher order modes in ducts driven above and below their cutoff frequency.
- Waves in Dispersive Media - when wave speed depends on frequency
- Examples of Dispersive Waves - Flexural waves and Quasi-longitudinal waves on a rod
- Interaction Between Two Solitary Waves - what is a soliton? and what happens when two solitons collide?
Room Acoustics
- Driving room modes & source location - How does the (resonance) response of a room depend on source location?
- Reverberation Time in a Small (but very reverberant) Room - audio files and plots for measurements of T60 in a small, empty room. [Updated: 1/17/2024]
- Reverb Times for a small Auditorium (page needs to be updated, but has measurements (and sound recordings) of T60 for a small theater at Kettering University)
Vibration and Structural Waves
Vibration of 1-DOF Simple Oscillators
- Comparing Circular and Sinusoidal Motion - how is circular motion in the complex plane (magnitude and phase) related to sine and cosine functions?
- Simple Harmonic Oscillator - with and without damping, transfer of energy between kinetic and potential forms
- Damped Harmonic Oscillator - underdamped, overdamped, and critically damped
- Phase-Space Diagrams for an Oscillator - plotting velocity v(t) as a function of position x(t)
- Forced Harmonic Oscillator - transient and steady state response to a force applied to the mass
- Base Motion - transient and steady state response of an oscillator to displacement of its support
- The Simple Pendulum - comparing the linear approximation (small angle) with a real pendulum.
- Crankshaft: Non-harmonic Oscillator - periodic oscillatory motion that is not sinusoidal.
- Regions of Resonance - interactive animation of the damping-controlled, stiffness-controlled, and mass-controlled regions in the displacement response of a forced mass-spring system.
Vibration of Multi-DOF Systems
- Coupled Oscillators - energy transfer between two mass-spring systems coupled together
- Dynamic Absorbers - J.P. Den Hartog's classical undamped tuned dynamic absorber
- Multiple-DOF mass-spring systems. - improved animation of the natural modes of a multi-degree-of-freedom mass-spring system.
Vibrational Modes of Continuous Systems
- Vibrational Modes of a Hanging Chain - mode shapes for a hanging chain
- The Plucked String (guitars) - mode shapes, Fourier Coefficients, and time signals for a plucked guitar string
- The Struck String (pianos) - the motion of a piano string after being struck by a hammer.
- The Bowed String (violins) - the Helmholtz motion of a bowed violin string
- Rectangular Membrane - Mode shapes for a rectangular membrane and degenerate modes of a square membrane
- Circular Membrane - or how a drum head vibrates.
- Membranes - vs - Strings: Initial Conditions Comparing the propagation of 2-D waves on a membrane with 1-D waves on a string for initial displacement and initial velocity conditions.
- Torsional Modes in a Rectangular Beam -- Twisting oscillation in a rectangular bar.
- Flexural Vibrations in a Rectangular Beam - flexural bending mode shapes and frequencies for a rectangular bar (New COMSOL animations 1/16/2024)
- Vibrational Modes of a Tuning Fork. - how does a tuning fork vibrate?
- Vibration of Baseball Bats - flexural bending modes and cylinder modes
Animations of Experimental Results
- Vibration Modes of a Glass Beer Bottle - what vibration shapes are responsible for the "clink" of a glass bear bottle?
- Bending and Torsional Vibration in a Hockey Stick - flexural bending and torsional twisting vibration in a hockey stick
- Vibrational Mode Shapes of a Racquetball Racket - Bending, Torsional and Membrane modes in a racquetball racket.
- Vibrational Mode Shapes of a Tennis Racket - Bending, Torsional and Membrane modes in a Tennis Racket.
- Vibrational Modes of an Electric Guitar - actual experimental data
- Vibrational Modes of an Acoustic Guitar - actual experimental data
- Vibrational Modes of a (cutlery) Fork -- Bending and Torsional vibration of a fork (the kind you eat with).
Miscellaneous Animations
- Motion of the Center-of-Mass - not exactly acoustics and vibration, but the animations are cool