PROPERTIES OF TRAVELLING WAVES Physics of Music, Spring 2015.

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Presentation transcript:

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: 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:

Plane waves and Circular Waves Image sources:Berg and Stork, Physics of Sound, 3 rd ed. CircularPlane 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=  x/  t  vT Or… v = f x Animation courtesy of Dr. Dan Russell, Kettering University Wavelength ( ): spatial distance from crest-to-crest Frequency (f): how many times per second one particular point oscillates

t = t o t = t o + 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 Brass3475 Sea Water1533 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  i =  r Angles measured with respect to the normal (dashed line perpendicular to the surface) Image sources:

Plane Wave Reflection and Ray Diagrams normal Ray diagram Image source:

Reflection from concave surface Image source: (left); Berg and Stork, Physics of Sound, 3 rd ed. (right)

Applications of Reflection? Image source: D. Hall, Musical Acoustics (left)

Diffraction Tendency for waves to spread out as a result of passing by an edge (barrier or passing through a slit) Image source: 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, 3 rd ed. (right) UC Irvine Optics research group.

Diffraction Patterns Diffraction in ripple tank Diffraction on a MUCH larger scale. Image sources: (top) =Q%201&show=1 =Q%201&show=1 Bottom:

Diffraction in Action