WAVES · PROPAGATION AND OSCILLATION
Mechanical waves: transverse and longitudinal
Explore a harmonic disturbance travelling through a uniform medium. Compare the motion of individual particles with the propagation of phase: the medium does not travel with the wave.
Physical parameters
Propagation through the medium
Colored dots represent medium particles: they oscillate perpendicular to the direction of propagation. The red dot marks the observed particle.
Medium profile (blue) and observed particle (red). Vertical displacement is magnified relative to the horizontal scale.
Continuum model: the displayed segment is not a string with fixed ends. Boundary conditions are not simulated.
Synchronized plots and time selection
Click a time plot to select t. Click the spatial profile to move the observed point.
Spatial profile u(x,t)
Particle oscillation u(xₚ,t)
Particle velocity ∂u/∂t
Particle acceleration ∂²u/∂t²
Sampled values
| t (s) | u (m) | vₚ (m/s) | aₚ (m/s²) | Compression (1) |
|---|
Assumptions and limitations
Ideal travelling harmonic waves in a uniform non-dispersive medium, with constant amplitude and no reflections, attenuation or net matter transport. Time is physical. Longitudinal compression is a first-order relative perturbation. Force, medium density and energy are not calculated because elastic and inertial properties were not specified.
WAVES · PROPAGATION AND OSCILLATION
Step-by-step worked solution
Every numerical substitution includes SI units. Phase is in radians; the initial angle is entered in degrees.