Waves

Physics 202Professor Lee

CarknerLecture 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 = ½mv2

Amplitude =xm, can get from total energy

Initial KE = max KE = total E = ½kxm

xm =(2E/k)½ = ([(2)(1250)]/(5000))½ = 0.71 m Equation of motion = x(t) = xmcos(t)

k = m2

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) = ym 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) = ym 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 = 2f and k = v = /k = 2f/2

v = f

i.e. v is the velocity of the wave form

Next Time

Read: 16.6-16.10

If the amplitude of a linear oscillator is doubled, what happens to the period?

a) Quarteredb) Halvedc) Stays the samed) Doublede) Quadrupled

If the amplitude of a linear oscillator is doubled, what happens to the spring constant?

a) Quarteredb) Halvedc) Stays the samed) Doublede) Quadrupled

If the amplitude of a linear oscillator is doubled, what happens to the total energy?

a) Quarteredb) Halvedc) Stays the samed) Doublede) Quadrupled

If the amplitude of a linear oscillator is doubled, what happens to the maximum velocity?

a) Quarteredb) Halvedc) Stays the samed) Doublede) Quadrupled

If the amplitude of a linear oscillator is doubled, what happens to the maximum acceleration?

a) Quarteredb) Halvedc) Stays the samed) Doublede) 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) Increaseb) Decreasec) 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) Increaseb) Decreasec) 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) Increaseb) Decreasec) Stay the same