1. 5.1.4 Interference, Standing Waves, and Resonance
Guitar Strings and Crumbling Bridges

2. 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

3. Example What is the direction of motion in the medium?
Both waves reach maximum
amplitude at that point!

4. Interference of Two Point Sources of Waves
When viewed from above, a wave source makes circular patterns
Ripple Tank
Simulation
TWO TROUGHS
CONSTRUCTIVE
crest (wave front)
trough
CRESTS AND TROUGH
DESTRUCTIVE
TWO CRESTS
CONSTRUCTIVE

5. 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.
Standing Waves

7. Practice
FOUR

8. 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.

13. 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

14. End of 5.1.4