Physic Labs

Oscillations and waves

Introduction to mechanical waves and the wave equation

Observe a transverse wave travelling along a string in the «Sóng cơ truyền trên dây» simulation: distinguish the oscillation of each string element about equilibrium from the propagation of the wave pattern. Read the slider values and verify v=λfv = \lambda f.

High school

Equipment

  • 3D canvas showing the wave shape on the string, rotated by dragging or arrow keys
  • Sliders «Biên độ A», «Bước sóng λ» and «Tần số f»
  • Readout line showing «Tốc độ truyền sóng v = λf»
  • «Tạm dừng» / «Chạy tiếp» button to freeze the wave shape

Procedure

  1. Watch wave travel versus local oscillation

    Keep «Tần số f» at a medium value and track a coloured patch on the canvas: each string element only moves up and down about its equilibrium while the whole wave pattern drifts along the string. Recognise that the wave transports energy and phase, not matter.

  2. Measure wavelength and frequency, check v = λf

    Set «Bước sóng λ» and «Tần số f» to two arbitrary levels, note the value beside each slider, and compare with the line «Tốc độ truyền sóng v = λf». Repeat with two other (λ, f) pairs and check v=λfv = \lambda f for every measurement.

  3. State the role of amplitude and predict the readout

    Press «Tạm dừng» to freeze the picture, count the wavelengths along the string and confirm that λ sets the crest-to-crest distance. Press «Chạy tiếp», change «Biên độ A» and show that the v readout does not depend on A — on a real string v is set by tension and linear density via v=T/μv = \sqrt{T/\mu}. Before changing f one last time, predict v and check the readout.

Simulation

Experiment history

Waves on a stretched string were first studied on instrument strings. Galileo Galilei noted how the pitch of a string relates to tension, length, and thickness in the final days of Dialogue Concerning Two New Sciences (1638). Brook Taylor in 1713 gave a mathematical basis for the periodic shape of a vibrating string. The decisive step was the wave equation ∂²y/∂t² = v² ∂²y/∂x² introduced by d'Alembert in 1747; Daniel Bernoulli then proposed representing the motion as a sum of harmonic modes, an idea Euler developed and Fourier generalised into series early in the 19th century. Isaac Newton in 1687 had already related wave speed to the elasticity and density of the medium, the basis for every model of oscillation propagating through matter.

Related physicists

Galileo GalileiIsaac NewtonLeonhard EulerDaniel Bernoulli

Related library topics

Introduction to mechanical waves and the wave equation