PROPERTIES OF
TRAVELLING WAVES
Physics of Music, Spring 2015
Key Terms
traveling 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
Wave
Transverse:
displacement is
perpendicular to
direction of wave
propagation
Spring image source:
http://www.factmonster.com/dk/science/encyclopedia/energy-waves.html
Animation 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 University
Long. Spring image source:
http://www.factmonster.com/dk/science/encyclopedia/energy-waves.html
Plane waves and Circular Waves
Circular
Plane
Where would you find them in musical context?
Image sources:Berg and Stork, Physics of Sound, 3rd ed.
A Day at the Beach
Check out the plane waves!!!
Travelling Waves
x
• Velocity (v): change in
position per change in time
• v= Dx/Dt
l = vT
• Or… v = lf
•
Frequency (f): how
many times per second
one particular point
oscillates
Wavelength (l):
spatial distance from
crest-to-crest
Animation courtesy of Dr. Dan Russell, Kettering University
𝑣
l = 𝑣𝑇
OR
t = to
𝑣 =lf
Physical Parameters
𝑣 [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]: frequency
How many oscillations per
second at one point in
space, f = 1/T.
l [m] = wavelength
How far between two crests
or two troughs
l
t = to + T
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)
Narrow aperture
Diffraction
Tendency for waves to
spread out as a result of
passing by an edge
(barrier or passing
through a slit)
Wide aperture
Image source: http://innovativescience.blogspot.com/2011/02/diffraction.html
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
Patterns
Diffraction in ripple tank
Diffraction on a MUCH
larger scale.
Image sources: (top)
http://scripts.mit.edu/~tsg/www/demo.php?letnum
=Q%201&show=1
Bottom: http://www.suntrek.org/factary/d.shtml
Diffraction in Action