2. PROPERTIES OF TRAVELLING WAVES Physics of Music, Spring 2015

3. Key Terms traveling wave transverse wave longitudinal wave plane waves circular waves velocity frequency wavelength Law of Reflection Huygent’s Principle: diffraction

4. 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

5. 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

6. 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

7. 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?

8. A Day at the Beach Check out the plane waves!!!

9. 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

10. t = t o t = t o + T

11. Travelling waves in ripple tank: high speed video (240 fps) Image from Arbor Scientific Ripple tank image, oblique view

12. Speed of Sound in Various Bulk Media Material Speed of Sound [m/s] Air (20 C)343 Brass3475 Sea Water1533 Wood~ 3600

13. Wave Mechanics: Acoustic Applications traveling wave transverse wave longitudinal wave plane waves circular waves velocity frequency wavelength Law of Reflection Huygent’s Principle: diffraction

14. Law of reflection  i =  r 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

15. Plane Wave Reflection and Ray Diagrams normal Ray diagram Image source: http://hyperphysics.phy-astr.gsu.edu/hbase/sound/reflec2.html#c1

16. Reflection from concave surface Image source: http://hyperphysics.phy-astr.gsu.edu/hbase/sound/reflec2.html#c1 (left); Berg and Stork, Physics of Sound, 3 rd ed. (right)http://hyperphysics.phy-astr.gsu.edu/hbase/sound/reflec2.html#c1

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

18. Diffraction Tendency 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

19. 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.

20. 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 http://scripts.mit.edu/~tsg/www/demo.php?letnum =Q%201&show=1 Bottom: http://www.suntrek.org/factary/d.shtml

21. Diffraction in Action