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