Waves Physics 202 Professor Lee Carkner Lecture 6

PAL #5 Damped SHM  Your view compared to face-on view Max x Min v Min x Max v  Where v is transverse velocity  Real x and v are constant (= x max and v max )

PAL #5 Damped SHM  What is r if v max = m/s and T = 3.6 days?    = 2  /T = 2  /(3.6)(24)(60)(60) = 2.02 X rad/sec   What is mass of planet?  Gravitational force = centripetal force   M = v 2 r/G = 1.9 X kg

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    Longitudinal waves are waves where the oscillations are parallel to the direction of travel  

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:  y m =  k =   =

Annotated Wave Equation

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

Period and Frequency  Period  Frequency  We will again use the angular frequency ,   The quantity (kx-  t) is called the phase of the wave

Wave Speed

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 

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