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