Definition, including nodes; the fundamental; and equations for first, second, and higher order harmonics.

Creating standing waves with first, second, and higher order harmonics by shaking a string up and down.

The fundamental and higher order harmonics, nodes, and the equation for a standing wave.

Create a standing wave by shaking a string and viewing it using strobe lights.

How wind instruments create sound using standing waves in the air, including a demonstration of a large pipe which creates sound after a copper grid in the pipe is heated and then cooled.

System response to a driving frequency; resonant frequency; resonance with and without damping.

Amplitude of shuttle on air track observed for high and low, then resonant, driving frequency.

Infinite coupled oscillators; harmonics; demonstration of first, second, third, sixth harmonics.

Harmonics in tubes which are closed, open at one end, open at both ends.

Music from tube open at both ends, wooden flute; Jingle Bells on wooden trombone.

Examples from life; tuning forks; breaking a wine glass with an appropriate sound frequency.

Video of the collapse of the first Tacoma Narrows Bridge.

Higher speed of sound in He allows higher voice.

Plane wave of E-field and B-field; satisfaction of wave equation with v = c; one-dimensional wave equation; standing waves.

4-part problem; finding A, f, p, v, λ, ν, and sketching the wave; finding transverse speed and standing waves.

Solution (PDF)

4-part problem; finding λ, ν, f, p and sketching; finding transverse speed and propagation speed.

Solution (PDF)

Finding the length of a flute necessary for specific note; valve spacing necessary for higher notes.

Solution (PDF)