5.1.4 Interference, Standing Waves, and Resonance

Guitar Strings and Crumbling Bridges

Introduction and Terms• INTERFERENCE – the result of two waves meeting in a

medium.– CONSTRUCTIVE – results in greater amplitude.– DESTRUCTIVE – results in lower amplitude.

• “In phase” interferes CONSTRUCTIVELY

• “180° out of phase” interferes DESTRUCTIVELY

ExampleWhat is the direction of motion in the medium?

D.Both waves reach maximum

amplitude at that point!

Interference of Two Point Sources of WavesWhen viewed from above, a wave source

makes circular patterns

crest (wave front)

trough

TWO TROUGHS CONSTRUCTIVE

TWO CRESTSCONSTRUCTIVE

CRESTS AND TROUGH DESTRUCTIVE

Phenomenon #3 – Standing Waves

• When a wave encounters a fixed boundary it REFLECTS.

• The reflected wave comes back through the original wave and they INTERFERE.

• The result is a STANDING WAVE. • NODES : always 180° out of phase (destructive

interference) - NO MOTION.• ANTINODES : alternate between in-phase and 180° out of

phase –MAX MOTION.

Practice

FOUR

Phenomenon #4 – Resonance• All mediums have a NATURAL FREQUENCY that

corresponds to their atomic structure.

• Exciting this frequency causes large AMPLITUDE vibrations in the medium

• If the frequency is excited with enough ENERGY the medium may become damaged or even shatter.

• If two materials have the same (or close) natural frequencies then vibrations may be passed from one material into the other.

Practice• The grid below represents a 10 meter long string.

– Sketch the standing wave that this string would produce if it were to have SIX nodes.

– Draw a circle around each ANTINODE on the string.– Determine the wavelength of this standing wave.

_________________m– Assuming that this wave moves at 2.0 meters per second,

calculate its frequency and period.

4

End of 5.1.4