Waves Physics 202 Professor Lee Carkner Lecture 6

Suppose you are watching Jupiter’s moon Io in a telescope. Where will Io appear to be moving fastest across the sky? a)When it is furthest away from Jupiter b)When it is closest to Jupiter c)When it is half the maximum distance away from Jupiter d)The speed is the same everywhere e)We can’t tell without more information

Which of the following would increase the rate at which a damped system loses energy the most? a)Doubling b b)Doubling m c)Halving b d)Halving m e)a and d only

Imagine a swing with a resonance at a period of T. What other period will also produce resonance? a)1/10 T b)¼ T c)½ T d)2 T e)2.5 T

PAL #5 Damped SHM  What is r if v max = m/s and T = 3.6 days?  v max =  x m so x m = v max /    = 2  /T = 2  /(3.6)(24)(60)(60) = 2.02 X rad/sec  x m =  What is mass of planet?  Gravitational force = centripetal force  GMm/r 2 = mv 2 /r  M = v 2 r/G =

Test Next Friday  About 15 multiple choice  Mostly concept questions  About 4 problems  Like PALs or homework  Bring calculator and pencil  Formulas and constants provided (but not labeled)  Worth 15% of grade

What is a Wave?   Example: transmitting energy,   A sound wave can also transmit energy but the original packet of air undergoes no net displacement

Transverse and Longitudinal  Transverse waves are waves where the oscillations are perpendicular to the direction of travel  Examples:   Longitudinal waves are waves where the oscillations are parallel to the direction of travel  Examples:  Sometimes called pressure waves

Transverse Wave

Longitudinal Wave

Waves and Medium   The wave has a net displacement but the medium does not   This only holds true for mechanical waves  Photons, electrons and other particles can travel as a wave with no medium (see Chapter 33)

Wave Properties   The y position is a function of both time and x position and can be represented as: y(x,t) = y m sin (kx-  t)  Where:   k = angular wave number 

Wavelength and Number   One wavelength must include a maximum and a minimum and cross the x-axis twice  k= 

Period and Frequency   Frequency is the number of oscillations (wavelengths) per second (f=1/T)   =2  /T  The quantity (kx-  t) is called the phase of the wave

Speed of a Wave  y(x,t) = y m sin (kx-  t)  But we want to know how fast the waveform moves along the x axis: v=dx/dt   If we wish to discuss the wave form (not the medium) then y = constant and:  e.g. the peak of the wave is when (kx-  t) =  /2  we want to know how fast the peak moves

Wave Speed

Velocity  We can take the derivative of this expression w.r.t time (t):  Since  = 2  f and k =  v =  /k = 2  f /2  v = f  Thus, the speed of the wave is the number of wavelengths per second times the length of each  i.e.

Next Time  Read:  Homework: Ch 16, P: 12, 15, 18, 24