Transcript Describing Waves

Combining Waves
interference
§ 14.7
Principle of Superposition
Where waves meet, the displacement is the
sum of the displacements from the individual
waves.
3
0
–3
result
Interference
• Constructive: Sum of waves has increased
amplitude
• Destructive: Sum of waves has decreased
amplitude
• Two-wave simulation
Interference Patterns
Interference of similar
wavelengths
Patterns
• Positions of constructive and destructive
interference
– destructive: nodes
– constructive: antinodes
• Ripple tank simulator
http://www.falstad.com/ripple/
Standing Waves
waves that don’t actually travel
§ 14.8
Standing Waves
• Sum of waves of equal amplitude and
wavelength traveling in opposite directions
• Half-wavelength divides exactly into the
available space
• Wave pattern has locations of minimum
and maximum variation (nodes and
antinodes)
• (standing longitudinal waves)
Normal modes
standing waves generalized
Modes
• Objects have characteristic frequencies at
which standing waves are sustained
• Lowest frequency = fundamental
• Higher frequencies = overtones
• Sustained motion is a combination of
normal modes
Vibrational Modes: Clamped
String
Source: Griffith, The Physics of Everyday Phenomena, Figure 15.13
Combinations of Harmonics
• Characteristic sounds arise from combining particular
harmonics in specific ratios
flute
Simulation
oboe
saxophone
“Closed” and “Open” Tube
Modes
Source: Halliday, Resnick, and Walker, Fundamentals of Physics, 2003, p 419.
Sequence of Harmonics
• Western musical scale and harmonies are
based on overtone series
• (sound files)
2-D Standing Waves
• Nodes are lines or curves
Circular membrane standing waves
edge node only
diameter node
circular node
Source: Dan Russel’s page
• Higher frequency  more nodes
Aside
• Electron orbitals in atoms and molecules
are 3-D standing waves
• All particles have wave natures
• Orbitals are interference patterns that
persist (don’t cancel over time)
• Stationary states are like harmonics
Resonance
• Boundary conditions determine nodal positions
• For uniform media, resonant wavelengths and
frequencies have simple relationships
– Clamped strings
– http://www.surendranath.org/Applets/Waves/Harmonics/HarmonicsApplet.html
– Air cylinders
– http://www.physics.smu.edu/~olness/www/05fall1320/applet/pipe-waves.html
• More complex media are more interesting
– http://paws.kettering.edu/~drussell/Demos.html
Beats
coincidence of similar frequencies
§ 14.9
Beats
• Waves of similar frequency combine to
give alternating times of constructive and
destructive interference
• Distinctive “waa-waa” sound with beat
frequency equal to the difference in
frequency of the component waves
fbeat = |f1 – f2|
• (Why?)
Beats
• Sound files
• Ripple tank simulator
http://www.falstad.com/ripple/