Physclips - Standing Waves

Links to related material and teachers' resources
Travelling waves, superposition, reflection and transmission Wave pulses in a stretched string. Equations for a travelling wave. Linear media. Superposition. The limits of linearity. Reflections at fixed and free boundaries. Reflection and transmission at step changes in density.
The travelling sine wave Describing the travelling sine wave. Comoving and fixed coordinates. y = sin (kx − ωt). Three dimensional plots. Phases in a travelling wave.
Waves in strings, reflections, standing waves and harmonics Plucked vs bowed strings. Mode diagrams and harmonics. Harmonic tuning on guitars. Touch fourths and natural harmonics.
Physics of the sound wave. Wave equation. Acoustic impedance Displacement, compression and pressure. Newton's second law and acceleration. The wave equation for sound. Speed of sound. Acoustic impedance.
Open vs closed pipes (Flutes vs clarinets) Reflection at open and closed ends. Mode diagrams for open-open and open-closed pipes. The harmonic series for flutes and clarinets. End effects. Real instruments and further complications.
Bows and strings The stick-slip cycle and Helmholtz motion. String speed at different positions. Bow force limits.
Music acoustics A web site introducing the physics of various instrument families, including the voice, and a range of related material.

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