General Wave Behavior

Physics of Music, Spring 2014

Key Termstraveling wave

transverse wave

longitudinal wave

plane waves

circular waves

Huygen's principle

reflection

diffraction

velocity

frequency

wavelength

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

Plane circular (diffraction!)

Image sources:(top) Berg and Stork, Physics of Sound, 3rd ed.(bottom) UC Irvine Optics research group.

Circular Plane

Huygen’s PrincipleA wavefront can be thought of as being composed by a large number of “wavelets”, each of which spread out spherically in time and space.

Image source: Berg and Stork, Physics of Sound, 3rd ed.

Law of reflectionAngle of incidence equals angle of reflection.

qi = qr

Both angles are 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

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

Key TermsWave Mechanics: Part II

traveling wave

transverse wave

longitudinal wave

plane waves

circular waves

Huygen's principle

reflection

diffraction

velocity

frequency

wavelength

A Day at the Beach

Check out the plane waves!!!

Travelling Wavesx

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

lf 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

𝑣t = to

t = to+ Tl

Travelling waves in ripple tank: high speed video (240 fps)

Image from Arbor ScientificRipple 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

Data from: http://www.engineeringtoolbox.com/sound-speed-solids-d_713.html