Waves Physics 202 Professor Lee Carkner Lecture 5

PAL #4 Pendulums  The initial kinetic energy is just the kinetic energy of the bullet   The initial velocity of the block comes from the kinetic energy  KE = ½mv 2   Amplitude =x m, can get from total energy  Initial KE = max KE = total E = ½kx m  x m =(2E/k) ½ = ([(2)(1250)]/(5000)) ½ = 0.71 m  Equation of motion = x(t) = x m cos(  t)  k = m  2   x(t) = 0.71 cos(31.6t)

Test Next Friday  About 15 multiple choice  Like Quizdom  About 4 problems  Like PALs or homework  Bring calculator and pencil  Formulas and constants provided (but not labeled)  Worth 10% of grade  I have put practice problems on webassign  Not for grade

Transverse Waves   Examples: waves on a string, ocean waves  Sometimes called shear waves

Longitudinal Waves   Examples: slinky, sound waves  Sometimes called pressure waves

Waves Properties   The wave has a net displacement but the medium does not   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   = angular frequency

Wavelength and Number   One wavelength must include a maximum and a minimum and cross the x-axis twice  We will often refer to the angular wave number k, 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: kx-  t = constant   we want to know how fast the peak moves

Wave Speed

Velocity  k(dx/dt) -  = 0 (dx/dt) =  /k = v  Since  = 2  f and k =  v =  /k = 2  f /2  v = f   i.e. v is the velocity of the wave form

Next Time  Read:

If the amplitude of a linear oscillator is doubled, what happens to the period? a)Quartered b)Halved c)Stays the same d)Doubled e)Quadrupled

If the amplitude of a linear oscillator is doubled, what happens to the spring constant? a)Quartered b)Halved c)Stays the same d)Doubled e)Quadrupled

If the amplitude of a linear oscillator is doubled, what happens to the total energy? a)Quartered b)Halved c)Stays the same d)Doubled e)Quadrupled

If the amplitude of a linear oscillator is doubled, what happens to the maximum velocity? a)Quartered b)Halved c)Stays the same d)Doubled e)Quadrupled

If the amplitude of a linear oscillator is doubled, what happens to the maximum acceleration? a)Quartered b)Halved c)Stays the same d)Doubled e)Quadrupled

If you have a pendulum of fixed mass and length and you increase the length of the path the mass travels, what happens to the period? a)Increase b)Decrease c)Stay the same

If you have a pendulum of fixed mass and length and you increase the length of the path the mass travels, what happens to the maximum velocity? a)Increase b)Decrease c)Stay the same

If you have a pendulum of fixed mass and length and you increase the length of the path the mass travels, what happens to the maximum acceleration? a)Increase b)Decrease c)Stay the same