Introduction to Waves

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1 Introduction to Waves 4 January 2016 PHYC 1290 Department of Physics and Atmospheric Science

2 Water waves Sound waves Radio waves Waves are everywhere in nature Visible Light X-rays Matter waves

3 Waves and Engineering Tacoma Narrows Bridge, 7 November

4 Demos Wave on a spring Torsion wave Wave on a string

5 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

6 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.

7 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).

8 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).

9 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.

10 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.

11 A history graph gives the displacements y as a function of time t for a specific position x.

12 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.

13 Media Credits %C3%B6lliker%27s_hand_-_ jpg

14 Extra Material

15 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.

16 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 x (m) Plot a history graph for the particle at x = 6 m.

17 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 x (m) After 1 s more, it travels 1 m more to the left: y (cm) t = 4 s x (m)

18 After 1 s more, it travels 1 m more to the left: y (cm) t = 5s 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) x = 6 m t (s)

Analytical Physics 1B Lecture 5: Physical Pendulums and Introduction to Mechanical Waves

Analytical Physics 1B Lecture 5: Physical Pendulums and Introduction to Mechanical Waves Sang-Wook Cheong Friday, February 16 th, 2017 Two Exam 1 Questions with errors Correct answer: L = r X p = (2000