Introduction to Waves 4 January 2016 PHYC 1290 Department of Physics and Atmospheric Science
Water waves Sound waves Radio waves Waves are everywhere in nature Visible Light X-rays Matter waves
Waves and Engineering Tacoma Narrows Bridge, 7 November 1940 http://youtu.be/a9lcu_zophq
Demos Wave on a spring Torsion wave Wave on a string
What is a wave? A traveling wave is an organized disturbance traveling at a well-defined phase speed v. e.g. 1: A wave pulse v e.g. 2: Periodic waves v
Wave Speed on a String For a string under tension T it can be shown that the phase speed v of a transverse wave is given by v = T µ where μ is the string s linear density μ = m/l (i.e., the mass per unit length). m is the string s mass and L is its length. The derivation of this equation will be given at the end of next day s lecture.
There are different kinds of waves Transverse waves have displacements y from equilibrium (rest) that are perpendicular to the direction of wave travel. y x The displacement depends on the position x v (usually measured from one end of the string).
Longitudinal waves have displacements y from equilibrium (rest) that are parallel to the direction of wave travel. Rarefaction Compression y v x The displacement depends on the position x (usually measured from one end of the string).
Wave Graphs Waves can be represented graphically in two different ways. A snapshot graph gives the displacements y as a function of position x at a specific instants in time t.
v = 5 m/s Let s plot a series of snapshots at different times t. Notice the displacement at x = 25 m changes with time. We can plot the displacement as a function of time.
A history graph gives the displacements y as a function of time t for a specific position x.
Students will be asked to convert history graphs to snapshot graphs, and vice-versa, on assignments and exams. There is an example in the Extra Material section at the end of this lecture. Exercise: Draw a history graph for the preceding example at x = 40 m.
Media Credits http://commons.wikimedia.org/wiki/file:2010_mavericks_competition.jpg http://commons.wikimedia.org/wiki/file:fa-18_hornet_breaking_sound_barrier_%287_july_1999%29.jpg http://commons.wikimedia.org/wiki/file:samsung_vibrant.png http://commons.wikimedia.org/wiki/file:double-alaskan-rainbow.jpg http://commons.wikimedia.org/wiki/file:x-ray_by_wilhelm_r%c3%b6ntgen_of_albert_von_k %C3%B6lliker%27s_hand_-_18960123-02.jpg http://commons.wikimedia.org/wiki/file:stylised_lithium_atom.svg
Extra Material
London Millennium Bridge Opening This video provides a fascinating discussion of what was learned by engineers when London s Millennium Bridge developed oscillations as thousands of people crossed it for the first time. http://www.youtube.com/watch?v=gqk21572osu
Snapshot to History Graph Example Consider the following snapshot graph of a wave that is traveling to the left at 1 m/s. y (cm) t = 0 s 0 2 4 6 8 10 x (m) Plot a history graph for the particle at x = 6 m.
We begin by plotting a series of snapshot graphs. After 3 s, the wave travels 3 m to the left: y (cm) t = 3 s 0 2 4 6 8 10 x (m) After 1 s more, it travels 1 m more to the left: y (cm) t = 4 s 0 2 4 6 8 10 x (m)
After 1 s more, it travels 1 m more to the left: y (cm) t = 5s 0 2 4 6 8 10 x (m) Notice that in this instant the particle at x = 6 m goes from maximum displacement back to the rest position. Finally, plot the displacements as a function of time: y (cm) 0 2 4 6 8 10 x = 6 m t (s)