Lect23 - Physics 211 Lecture 23 Today's Concepts Harmonic...

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Unformatted text preview: Physics 211 Lecture 23 Today's Concepts: Harmonic Waves Physics 211 Lecture 23, Slide 1 Physics "Everything. Especially the differential equations. Also, how to use these "Everything. use concepts in problem solving." Are we going to learn fluids? There are fluid equations on the formula sheet. go through the main equation and how to use it. "y(x,t) = Acos(kx-wt)" Well, the semester's almost over, and I still haven't gotten on the board. Thank you for forcing us to actually watch the prelectures and pay attention to the and material before coming to class. I always hated watching them and I still do, but I think it really helps me learn. The one thing you could improve is getting the scripts up earlier; I think I learn better from them than from videos. more stadium wave stuff. it's a good way to spend 2 or 3 minutes. Will there be a review session at all during the weekend or extended office hours since there is no review session during lectures this week? I'm still hoping that you could put up an iclicker question asking the class if question they think my ex girlfriend and I should get back together. I visited her this weekend and things went very well, I think she's really close to taking me back taking and I just think some hard evidence would help to persuade her. If the majority of the smartest students at U of I all agree that we should get back together then there's no way she can turn me down. If you have a few minutes before or after class I would greatly appreciate the help. I can't BELIEVE we have homework due on the day finals begin. Can we get a can't BREAK??? AND we have no discussion.... Two guys approach a bar. The first guy walks into it. The second guy ducks. guy Why does velocity not depend on amplitude, frequency, and wavelength? PLEASE ANSWER THIS QUESTION!!!!!!! Is it possible to download the prelectures to save them?? It would be really convenient to keep them as to reference in the future, like an old textbook. It would be a shame to lose them once done with this class. I think you said something about Red Hot Chili Peppers before class last time but I missed what you said =( This time maybe? =D PLEASE?! (I'm running out of lectures!) How does direction affect the functional form? I'm really confused on the preflight #5. flight While I was watching the prelecture, I would pause in between slides to gently shake my mug of cider and observe the waves as they went across the surface. Thanks for more useful real-world knowledge. =P How do we prepare for the final exam???? Give us the direction!!! How I really don't like my roommate. How do I get rid of him without getting sent to getting jail? A LOT OF EXAMPLES WITH DETAILS ON PERIOD, WAVE #, SPEED OF WAVE. do we have to know the wave equation or is that just a proof for the speed on the wave on a string equation? and!! can you give us hints on the hw again...it IS the last one. let's all get 100% on them! :D Waves travel by way of a medium. What then is the medium that light travels through in space which is a vaccum? Two atoms bump into each other. One says 'I think I lost an electron!' The other asks, 'Are you sure?', to which the first replies, 'I'm positive.' "Can we please do the wave in lecture??? I think that would make up for the up fact that there is no lab this week!" "The only waves I know of are radio waves and ocean waves... Can you you explain all the waves, like the ones in the prelecture? Thank You!" What is a wave ? What A wave is a traveling disturbance that transports energy but not matter. • Examples: Examples: –Sound waves (air moves back & forth) –Stadium waves (people move up & down) –Water waves (water moves up & down) –Light waves (what moves??) Physics 211 Lecture 23, Slide 6 Types of Waves Types Transverse: The medium oscillates perpendicular to the direction the wave is moving. This is what we study in Physics 211. Movie (twave) Longitudinal: The medium oscillates in the same The direction as the wave is moving. Movie (lwave) Physics 211 Lecture 23, Slide 7 Wavelength: The distance λ between identical points on the wave. between Amplitude: The maximum displacement A of a point on the wave. of Period: The time P it takes for an element of the medium to make it one complete oscillation. y = A cos(kx − ωt ) Wave Properties Wave Movie (tspeed) Wavelength λ A 2π = 2πf ω= P λω = v= Pk T k= 2π λ String: v = μ Physics 211 Lecture 23, Slide 9 Preflight y A y x x B Waves A and B shown above are propagating in the same Waves medium. How do their frequencies compare? A) ωA < ωB B) ωA = ωB C) ωA > ωB Physics 211 Lecture 23, Slide 10 y A y x x B Waves A and B shown above are propagating in the same Waves medium. How do their frequencies compare? B) ωA = ωB C) ωA > ωB A) ωA < ωB B) C) A) A) velocity=frequency*wavelength. Both have the same velocity, so omega a is less than omega b because it has a longer wavelength B) They are the same because they are moving in the same medium C) shorter the wavelength, higher the frequency Physics 211 Lecture 23, Slide 11 Act The speed of sound in air is a bit over 300 m/s, and the The 300 speed of light in air is about 300,000,000 m/s. 300,000,000 Suppose we make a sound wave and a light wave that both have a wavelength of 3 meters. What is the ratio of meters the frequency of the light wave to that of the sound wave? (A) About 1,000,000 (B) About 0.000001 (C) About 1000 Physics 211 Lecture 23, Slide 12 How to make a function move How y Suppose we have some function y = f(x): 0 x y f(x - a) is just the same shape moved f(x a distance a to the right: 0 x=a x Let a = vt Then Let vt f(x - vt) will describe the same vt will shape moving to the right with speed v. y v 0 x = vt x Physics 211 Lecture 23, Slide 13 For a harmonic wave: For Consider a wave that is harmonic in x and has a wavelength of λ. y A λ x If the amplitude is maximum at ⎛ 2π ⎞ x⎟ x = 0 this has the functional form: y ( x) = A cos⎜ this ⎝λ ⎠ y v x Now, if this is moving to the right with speed v it will the it be described by: ⎛ 2π ⎞ y ( x) = A cos ⎜ ( x − vt ) ⎟ = A cos(kx − ωt ) ⎝λ ⎠ Physics 211 Lecture 23, Slide 14 Act If a function moving to the right with speed If v is described by f(x - vt) then what is f(x vt then describes the same function moving to the left with speed v ? y y = f(x - vt) vt v 0 x y A) y = - f(x - vt) f(x vt B) y = f(x + vt) vt 0 v x C) y = f(-x + vt) vt Suppose the function has its maximum at f(0). Suppose f(0). y = f(x - vt) vt x – vt = 0 vt x = vt x – vt = 0 vt x = vt y v y 0 x A) y = - f(x - vt) f( v 0 v x B) y = f(x + vt) x + vt = 0 x = -vt -x + vt = 0 x = vt v y v C) y = f(-x + vt) v 0 x Moves to the right when the signs in front of the x and t terms are different Moves to the left when the signs in front of the x and t terms are the same Preflight y A x We have shown that the functional form y(x,t) = Acos(kx-wt) We represents a wave moving in the +x direction. direction. Which of the following represents a wave moving in the –x direction? direction? A) y(x,t) = Acos(wt-kx) B) y(x,t) = Asin(kx-wt) C) y(x,t) = Acos(kx+wt) Physics 211 Lecture 23, Slide 17 Energy Energy Preflight y A y x x B Waves A and B shown above are propagating in the same Waves medium with the same amplitude. Which one carries the most energy per unit length? A) A B) B C) They carry the same energy per unit length Physics 211 Lecture 23, Slide 19 y A y x x B Which one carries the most energy per unit length? Which A) A B) B C) Same C) A) Less frequency, more energy. B) kinetic energy is proportional to w^2A^2 ... same A, bigger w in B in C) There is no C, silly. Physics 211 Lecture 23, Slide 20 y = A cos(kx − ωt ) 2π λ= k v= ω k Look at signs in front of x and t Physics 211 Lecture 21, Slide 21 ω f= 2π y = A cos(kx − ωt ) dy vy = = ω A sin(kx − ωt ) dt ay = dv y dt = −ω 2 A cos(kx − ωt ) Physics 211 Lecture 21, Slide 22 Physics ω2 T =2 v2 = = μ mL k T θ Fy = 2T sin θ ≈ 2Tθ ≈ 2T tan θ dy ≈ 2T dx ≈ 2TkA y = A cos(kx − t ) dy = − kA sin(kx − ωt ) dtx dy = kA dx max Physics 211 Lecture 21, Slide 23 Physics ...
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This note was uploaded on 09/22/2011 for the course PHYSICS 211 taught by Professor Selig during the Fall '10 term at University of Illinois, Urbana Champaign.

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