Interference
Physics 2A
Superposition and
Standing Waves
⇒ If two waves exist at
the same point in space
at the same time, they
will interfere with each
other.
Interference
Beats
Standing Waves on a String
animations
Interference
Superposition Principle for Waves
⇒ Overlapping waves do not alter the travel of the
other wave.
The Principle of Linear Superposition : When two or more waves
are present simultaneously at the same place, the resultant disturbance
is the sum of the disturbances from the individual waves.
⇒ The individual waves move independently
of one another.
1
Interference
Interference
⇒ Sound waves, like any waves, can interfere
with each other.
Constructive
Interference
Constructive
Interference
Destructive
Interference
Interference
Destructive
Interference
Beats
⇒ Constructive interference occurs when the
condensations (or the rarefactions) from two sounds waves overlap.
⇒ Destructive interference occurs if the condensation from one
⇒ If two sound waves with slightly different frequencies
sound wave overlaps the rarefaction from another sound wave.
overlap, the interference of the two sound waves produce
beats.
2
Reflections at a Boundary
Beats
f = 10 Hz
f = 12 Hz
f = 2 Hz
⇒ When a wave hits a hard boundary like a wall that
is too rigid to shake, the wave will reflect back.
⇒ If we continue producing waves, the incident
beat frequency = difference in the two frequencies
Standing Waves
waves and the reflected waves will interfere with each
other.
Standing Waves
antinodes
nodes
3
Standing Waves
Standing Waves
fundamental mode or first harmonic
second harmonic
Standing Waves
third harmonic
4