1. Class 38 - Waves I Chapter 16 - Wednesday November 24th Reading: pages 413 to 423 (chapter 16) in HRW Read and understand the sample problems Assigned problems from chapter 16 (due Dec. 2nd): 6, 20, 22, 24, 30, 34, 42, 44, 66, 70, 78, 82 Traveling waves Waves on a string The wave equation Sample problems Exam 3: Friday December 3rd, 8:20pm to 10:20pmExam 3: Friday December 3rd, 8:20pm to 10:20pm You must go to the following locations based on the 1st letter of your last name:You must go to the following locations based on the 1st letter of your last name: Review sessions: Tues. Nov. 30 and Thurs. Dec. 2, 6:15 to 8:10pmReview sessions: Tues. Nov. 30 and Thurs. Dec. 2, 6:15 to 8:10pm

2. Waves I - types of waves 1.Mechanical waves: water waves, sound waves, seismic waves. 2.Electromagnetic waves: radio waves, visible light, ultraviolet light, x-rays, gamma rays. 3.Matter waves: electrons, protons, neutrons, anti-protons, etc.. 1.These are the most familiar. We encounter them every day. The common feature of all mechanical waves is that they are governed entirely by Newton's laws, and can exist only within a material medium. 2.All electromagnetic waves travel through vacuum at the same speed c, the speed of light, where c = 299 792 458 m/s. Electromagnetic waves are governed by Maxwell's equations (PHY 2049). 3.Although one thinks of matter as being made up from particles, it is in fact made up from fundamental matter waves that travel in vacuum. Matter waves are governed by the laws of quantum mechanics, or the Schrödinger and Dirac equations.

3. Wave interference Matter-wave interference

4. Waves I - types of waves Transverse waves (2 polarizations) Longitudinal waves

5. Waves I - wavelength and frequency Wavelength (consider wave at t = 0 ): You can always add 2  to the phase of a wave without changing its displacement, i.e. Transverse sinusoidal wave phase shift

6. Waves I - wavelength and frequency Wavelength (consider wave at t = 0 ): We call k the angular wavenumber. The SI unit is radian per meter, or meter -1. This k is NOT the same as spring constant. Transverse sinusoidal wave phase shift

7. Waves I - wavelength and frequency Period and frequency (consider wave at x = 0 ): Again, we can add 2  to the phase, Transverse sinusoidal wave phase shift

8. Waves I - wavelength and frequency Period and frequency (consider wave at x = 0 ): We call  the angular frequency. The SI unit is radian per second. The frequency f is defined as 1/T. Transverse sinusoidal wave phase shift

9. The speed of a traveling wave A fixed point on a wave has a constant value of the phase, i.e.A fixed point on a wave has a constant value of the phase, i.e. Or Transverse sinusoidal wave

10. The speed of a traveling wave For a wave traveling in the opposite direction, we simply set time to run backwards, i.e. replace t with  t.For a wave traveling in the opposite direction, we simply set time to run backwards, i.e. replace t with  t. So, general sinusoidal solution is:So, general sinusoidal solution is: In fact, any function of the formIn fact, any function of the form is a solution. Transverse sinusoidal wave

11. Traveling waves on a stretched string  is the string's linear density, or force per unit length. Dimensional analysis Tension  provides the restoring force (kg.m.s -2 ) in the string. Without tension, the wave could not propagate.Tension  provides the restoring force (kg.m.s -2 ) in the string. Without tension, the wave could not propagate. The mass per unit length  (kg.m -1 ) determines the response of the string to the restoring force (tension), through Newtorn's 2nd law.The mass per unit length  (kg.m -1 ) determines the response of the string to the restoring force (tension), through Newtorn's 2nd law. Look for combinations of  and  that give dimensions of speed (m.s -1 ).Look for combinations of  and  that give dimensions of speed (m.s -1 ).

12. Traveling waves on a string The tension in the string is .The tension in the string is . The mass of the element dm is  dl, where  is the mass per unit length of the string.The mass of the element dm is  dl, where  is the mass per unit length of the string. x y

13. Traveling waves on a string In the small  limit...In the small  limit... x y

14. The wave equation General solution:General solution: