Existence of periodic travelling waves solutions in predator
PROPERTIES OF TRAVELLING WAVES Physics of Music, Spring 2015.
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Transcript of PROPERTIES OF TRAVELLING WAVES Physics of Music, Spring 2015.
PROPERTIES OF TRAVELLING WAVESPhysics of Music, Spring 2015
Key Termstraveling wave
transverse wave
longitudinal wave
plane waves
circular waves
velocity
frequency
wavelength
Law of Reflection
Huygent’s Principle: diffraction
What is a traveling wave?A disturbance which travels through a medium, transmitting energy from the source to the observer without any net transfer of mass.
Animation courtesy of Dr. Dan Russell, Kettering University
Transverse WaveTransverse: displacement is perpendicular to direction of wave propagation
Spring image source: http://www.factmonster.com/dk/science/encyclopedia/energy-waves.htmlAnimation courtesy of Dr. Dan Russell, Kettering University
Longitudinal Wave
Longitudinal: displacement is parallel to direction of wave propagation.
Animation courtesy of Dr. Dan Russell, Kettering UniversityLong. Spring image source: http://www.factmonster.com/dk/science/encyclopedia/energy-waves.html
Plane waves and Circular Waves
Image sources:Berg and Stork, Physics of Sound, 3rd ed.
Circular Plane
Where would you find them in musical context?
A Day at the Beach
Check out the plane waves!!!
Travelling Waves• Velocity (v): change in position
per change in time• v= Dx/Dt
• = l vT• Or… v = lf
x
Animation courtesy of Dr. Dan Russell, Kettering University
Wavelength (l): spatial distance from crest-to-crest
Frequency (f): how many times per second one particular point oscillates
Physical Parameters
[m/s] : velocity How far a wavefront travels per unit time, Dx/Dt. Property of the medium/material.
T [s]: period How much time elapses between generation of each pulse (wavefront)
f [Hz]: frequencyHow many oscillations per second at one point in space, f = 1/T.
l [m] = wavelengthHow far between two crests or two troughs
l OR lf 𝑣
t = to
t = to+ Tl
Travelling waves in ripple tank: high speed video (240 fps)
Image from Arbor Scientific Ripple tank image, oblique view
Speed of Sound in Various Bulk Media
Material Speed of Sound [m/s]
Air (20 C) 343
Brass 3475
Sea Water 1533
Wood ~ 3600
Wave Mechanics: Acoustic Applications
traveling wave
transverse wave
longitudinal wave
plane waves
circular waves
velocity
frequency
wavelength
Law of Reflection
Huygent’s Principle: diffraction
Law of reflection
qi = qr
Angles measured with respect to the normal (dashed line perpendicular to the surface)
Image sources:http://www.dl.ket.org/physics/companion/thepc/compan/Light/Light-t.htm
http://www.worsleyschool.net/science/files/reflectionlaw/page.html
Plane Wave Reflection and Ray Diagrams
normal
Ray diagram
Image source: http://hyperphysics.phy-astr.gsu.edu/hbase/sound/reflec2.html#c1
Reflection from concave surface
Image source: http://hyperphysics.phy-astr.gsu.edu/hbase/sound/reflec2.html#c1 (left); Berg and Stork, Physics of Sound, 3rd ed. (right)
Applications of Reflection?
Image source: D. Hall, Musical Acoustics (left)
DiffractionTendency for waves to spread out as a result of passing by an edge (barrier or passing through a slit)
Image source: http://innovativescience.blogspot.com/2011/02/diffraction.html
Narrow aperture
Wide aperture
Huygen’s Principle
Wavefront = many wavelets spherically spreading out
Plane circular (diffraction!)
Image sources:(left and middle) Berg and Stork, Physics of Sound, 3rd ed.(right) UC Irvine Optics research group.
Diffraction PatternsDiffraction in ripple tank
Diffraction on a MUCH larger scale.
Image sources: (top) http://scripts.mit.edu/~tsg/www/demo.php?letnum=Q%201&show=1Bottom: http://www.suntrek.org/factary/d.shtml
Diffraction in Action