Waves

1. Waves Today�s Big Four: Waves are propagating disturbances They are wiggles in both time and space Waves transfer energy, not mass How to describe waves Superposition of waves Mention mechanical, E&M, matter waves (ie: QM) Need a few easy ponderables relating wave speed, frequency and wavelength Steal some CQ from TP or PIMention mechanical, E&M, matter waves (ie: QM) Need a few easy ponderables relating wave speed, frequency and wavelength Steal some CQ from TP or PI

2. Equations:

3. Transverse and longitudinal waves

4. Mathematical Description Suppose we have some function y = f(x):

5. Mathematical Description

6. Mechanical waves a disturbance that propagates through a medium

7. Periodic mechanical waves a disturbance that propagates through a medium, repeating itself over time a special case is where each of the particles undergoes SHM - then the wave is said to be sinusoidal

8. Summary: The wave function

11. Problem 1: wavelength, period and wave speed: Open superpos.html Work problem 1. Use �test your function here� to explore how the wave function changes if you: 1.Double the amplitude. 2.Double the wave length ?. 3.Doube the frequency f. 4.Change the phase constant F from 0 to pi.

12. Problem 2: Wavelength and speed

13. Problem 3: Sinusoidal Waves A sinusoidal wave of frequency 425 Hz has a velocity of 310 m/s. How far apart are two points that differ in phase by p/3 rad? (Here times are the same) (b)What is the phase difference between two displacements at a certain point at times 1.00 ms apart? (Here positions are the same) 0.122 m 2.67 rad Skip it. Too technical.0.122 m 2.67 rad Skip it. Too technical.

14. Problem 4: Wave speed A weight is hung over a pulley and attached to a string composed of two parts, each made of the same material but one having four times the diameter of the other. The string is plucked so that a pulse moves along it, moving at speed v1 in the thick part and at speed v2 in the thin part. Calculate v1/v2. Make reference to piano or guitar stringsMake reference to piano or guitar strings

15. Principal of superposition two waves traveling on the same rope meet each other Superposition: we add(vectorally) the displacements of eachwave to make a total displacement energy transfer by work done by bits of ropeenergy transfer by work done by bits of rope

16. Superposition

17. Notice that the sum wave (in blue) is a travelling wave which moves from left to right. When the two gray waves are in phase the result is a large amplitude. When the two gray waves become out of phase the sum wave is zero.

18. Superposition: Standing wave When the two waves are 180� out-of-phase with each other they cancel, and when they are in-phase with each other they add together. As the two waves pass through each other, the net result alternates between zero and some maximum amplitude. This pattern simply oscillates; it does not travel to the right or the left. Two sinusoidal waves having the same frequency (wavelength) and the same amplitude are travelling in opposite directions in the same.

19. Problem 5: Standing wave Two harmonic waves with same amplitude and frequency are travelling on the same rope but in opposite direction. Show that as they meet each other, they create a standing wave. Use the principle of superposition and the trigonometric identity: Acos(a)+Acos(b) = 2Acos[(a-b)/2] cos[(a+b)/2] .

20. Problem 6: Standing wave Open superpos.html Work problem 2 Check if your resulting wave has a node in the middle. If not, how much do you need to shift the wave function in the middle panel in order to move the node of the superimposed function to the middle? Acos(a)+Acos(b) = 2Acos[(a-b)/2] cos[(a+b)/2] .

21. Problem 7: Different constant phases What phase difference between two otherwise identical traveling waves, moving in the same direction along a stretched string, will result in the combined wave having an amplitude 1.30 times that of the common amplitude of the two combining waves? Express your answer in degrees. 98.9 degrees Ick! Replace this with a graphic question showing two waves and asking how they add.98.9 degrees Ick! Replace this with a graphic question showing two waves and asking how they add.

22. Superposition: Beats

23. Problem 8:Beats Open superpos.html Work problem 3 Acos(a)+Acos(b) = 2Acos[(a-b)/2] cos[(a+b)/2] .

24. Reflections what happens if a wave reaches a boundary, e.g. the fixed end of a rope? energy transfer by work done by bits of rope We can motivate this better with a more physical argumentenergy transfer by work done by bits of rope We can motivate this better with a more physical argument

25. Standing waves if we fix both ends of a string, what sort of waves do we get? energy transfer by work done by bits of ropeenergy transfer by work done by bits of rope

26. Problem 9: a giant bass violRemember A string of length 5.00m between fixed points, has mass per unit length 40.0g/m and a fundamental frequency of 20.0 Hz. what is the tension in the string? what is the frequency and the wavelength of the second harmonic? what is the frequency and wavelength of the �second overtone�? energy transfer by work done by bits of ropeenergy transfer by work done by bits of rope

35. Lab report Names and roles (1point) Physics 2211-Course number Title (max 2 points) Abstract (max 15 points) Introduction (max 5 points) Materials and methods (max 10 points)

36. Lab report Reporting the results (max 10 points) Copy and finish table 1, 2,3. Finish the analysis:

37. Lab report Discussion (max 10 points) Conclusion (max 10 points) Data (max 10 points) Presentation (max 10 points) Overall impact (max 10 points)