Standing waves & Resonance

wave speed equation

v = wavelength/frequency

Wave speed equation 2

v = displacement/time

Standing Waves

When a wave overlaps and interferes with its own reflection returning from a system/container boundary

How do standing waves look?

appear to stay in place bouncing up and down in distinct loops

n loops =

nth harmonic

nodes

points with zero movement

anti-node

points that show the maximum displacement

Resonance

When the driving frequency matches a system/containers natural frequency

If the medium has no dampening properties (ie.: inertia, tension)

every reflection of the wave puts more energy into the standing wave

As energy in standing waves increases

amplitude will increase dramatically

Fixed Boundaries Rule (Guitar String)

Ends are clamped down (must have a node)

Fixed Boundaries Harmonic Condition

Whole loops must fit with the length L of the string (wavelength n = 2L/n)

Open Boundaries Rule (Flute)

Air molecules can move freely in and out of open ends (must have an anti-node at both ends)

Open Boundaries Harmonic Condition

Whole loops must fit in the length of the air column (wavelength n = 2L/n)

Asymmetric Boundaries Rule (Clarinet)

Fixed end - must have node Open end - must have anti-node

Asymmetric Harmonic Condition

loops can only be odd number integer amounts, even loops requires symmetric ends (wavelength n = 4L/n)