Announcements 10410 Prayer n Exam goes until Saturday

Announcements 10/4/10 Prayer n Exam goes until Saturday – Correction to syllabus: on Saturdays, the Testing Center gives out last exam at 3 pm, closes at 4 pm. n Complex numbers next time. The Colton “Complex numbers summary” should be helpful. (We’ll go over today, if enough time. ) n Homework survey n

k and w n What’s the difference between these: n General form of cosine wave: …sometimes written as: n k = “wavevector”; w = “angular frequency” w=…

Quick Writing n If I have a longitudinal wave passing down my slinky, described by the function s(x, t), what does s represent, what does x represent, and what does t represent? n Other good questions: For a fixed time, what would s(x) represent? For a fixed x, what would s(t) represent?

Demos Shive wave machine n Web demo: n http: //www. colorado. edu/physics/phet/simulations/stringwave/string. Wave. swf

Reminder: the Wave Equation n Any function that has “x-vt” will work! …or “x+vt” Why is it called the wave equation? – Because traveling waves are solutions of the equation!

Analysis: A section of rope 1 T 2 T 1 T 2 q = small; cosq 1 x x+Dx q 1 T 1 m = mass/length “linear mass density” 1 q = small; sinq tanq

A section of rope, cont. T 2 T 1 T 2 q 1 T 1 x x+Dx What is tanq 2 in picture? tanq 2 = opp/adj = rise/run = slope! (at x + Dx)

Demo: wave speed vs tension n. I think mass of spring is 0. 276 kg. (Check with balance. ) n Can we predict how fast wave will travel?

Reading Quiz n A wave pulse traveling on a string hits the end of the string, which is tied to a post. What happens? – The pulse reflects, flipped over – The pulse reflects, not flipped over

Reading Quiz n A wave pulse traveling on a string meets an interface, where the medium abruptly switches to a thicker string. What happens? – The pulse continues on, but flipped over – The pulse continues on, not flipped over – The pulse reflects, not flipped over – The pulse partially reflects and partially transmits Advertisement: We’ll figure out the equations for reflection and transmission on Friday

Power: energy transfer n (Proved in book; most important is P ~ A 2)

The Wave Equation: Linear Any function that has “x-vt” will work! Why is it called the linear wave equation? – Because we don’t have nonlinear terms like f 2, x f, ex, etc. , in the equation itself. n Properties of linear differential equations: – If f 1 is a solution, then so is C f 1 – f 1 and f 2 are solutions, then so is (f 1+f 2). Consider: n

Thought Question n What happens when two wave pulses on a linear medium run into each other head on? – They reflect off of each other and go back the way they came. – Part of each wave is reflected and part transmitted. – They pass right through each other. Demo: Shive wave machine interference n Web demo again n

Complex Numbers – A Summary n n n What is “i”? What is “-i”? The complex plane Complex conjugate – Graphically, complex conjugate = ? Polar vs. rectangular coordinates – Angle notation, “A q” Euler’s equation…proof that eiq = cosq + isinq – must be in radians