Chapter 11: vibrations and waves - PowerPoint PPT Presentation

1 / 30
About This Presentation
Title:

Chapter 11: vibrations and waves

Description:

The spring will slowly return to its equilibrium position. ... a train of freight cars, each 10 m long, rolls by you at the rate of 2 cars each ... – PowerPoint PPT presentation

Number of Views:318
Avg rating:3.0/5.0
Slides: 31
Provided by: laur386
Category:

less

Transcript and Presenter's Notes

Title: Chapter 11: vibrations and waves


1
Chapter 11 vibrations and waves
2
Hookes Law
  • The spring force and the distance that the spring
    is stretched are proportional but opposite in
    direction.
  • Felastic kx
  • Felastic is the spring force (N), k is the spring
    constant (N/m), and x is the displacement (m).

3
Simple Harmonic Motion
  • Simple harmonic motion describes any periodic
    motion that is a result of a restoring force that
    is proportional to displacement.
  • In simpler terms, simple harmonic motion
    describes a back and forth motion that occurs
    over the same path (any vibration is an example
    of simple harmonic motion).
  • Whenever a back and forth motion occurs and a
    restoring force pushes an object back to its
    equilibrium position, simple harmonic motion
    occurs.

4
  • A pendulum is an example of simple harmonic
    motion.
  • It has a back-and-forth motion
  • It has a restoring force (the x component of
    gravity acting on the bob) that pulls the bob
    back to its equilibrium position.
  • However, this is only true for small angles of ?.
    (Only when ? lt 15)

5
Do Now 3/9/09
  • Which of these periodic motions are simple
    harmonic?
  • (a) A child swinging on a playground swing (?
    45)
  • (b) A CD rotating in a player
  • (c) An oscillating clock pendulum (? 10)

6
Amplitude, Period, Frequency
  • The amplitude is the maximum displacement from an
    equilibrium position.
  • The period, T, is the time it takes for a
    complete cycle to occur.
  • The frequency, f, is the number of cycles that
    occur in a specific unit of time (usually
    seconds). Frequency is measured in Hertz (Hz).
  • If a wave completes one cycle in 2 seconds, how
    many cycles occur in one second?

7
  • If a wave completes one cycle in 4 seconds, how
    many cycles occur in one second?
  • If a wave complete one cycle in 10 seconds, how
    many cycles occur in one second?
  • What do you notice about the period and frequency
    in each situation?

8
  • Period (T) and Frequency (f) are inverses of each
    other
  • f 1/T
  • T 1/f
  • Group Activity
  • Decide whether your two pendulums have the same
    period.

9
Period of a Pendulum
  • The period of a pendulum only depends on the
    pendulums length, not the mass.
  • Two pendulums with different masses will have the
    same period. But two pendulums with different
    lengths will have different periods.
  • When the length of a pendulum is decreased, so is
    the distance to the equilibrium position, so it
    takes a shorter amount of time for the short
    pendulum to reach equilibrium. The shorter
    pendulum will have a shorter period.

10
Do Now 3/10/09
  • 1.) A pendulum that moves through its equilibrium
    position once every 1 second is sometimes called
    a seconds pendulum.
  • (a)What is the period of any seconds pendulum?
  • (b)In Cambridge, England, a seconds pendulum is
    0.9942 m long. What is the free-fall
    acceleration in Cambridge?

11
Period of a Mass-Spring System
  • Mass affects the period of a mass-spring system.
  • The heavier the mass that hangs from a spring,
    the more resistance the spring has to going back
    to its equilibrium position. The spring will
    slowly return to its equilibrium position.
  • A heavy mass has a small acceleration, which
    means it takes longer to complete one cycle of
    motion.
  • If a lighter mass is attached to a spring, there
    is little resistance to restoring to the
    equilibrium position. A lighter mass will cause
    the spring to return to equilibrium much faster.
  • A light mass has a bigger acceleration, which
    means that it takes a shorter amount of time to
    complete one cycle of motion.
  • The period of a heavy mass-spring system will be
    longer than the period of a light mass-spring
    system.

12
Period of Mass-Spring System
  • Stiffer springs will take less time to return to
    equilibrium, which means that they will take less
    time to complete one cycle of motion (Stiffer
    springs will have shorter periods).
  • Flexible springs will take more time to return to
    equilibrium, which means that they will take more
    time to complete one cycle of motion (Flexible
    springs will have longer periods).

13
Medium
  • Waves are caused by a disturbance in some object
    or material.
  • In order to transfer energy, most waves must
    travel through a medium.
  • A medium is an object or material that the
    disturbance passes through.
  • Once the disturbance passes through a medium, the
    medium will return to its original position or
    shape.

14
Types of Waves
  • Transverse Waves occur when the motion of the
    medium (such as a slinky) is perpendicular to the
    direction in which the wave travels.
  • The slinky moves up and down in a vertical
    direction, but the wave is moving horizontally
    down the slinky.
  • Longitudinal Waves occur when the medium moves in
    the same direction in which the wave travels. The
    medium moves along the direction of the wave
    instead of perpendicular to it.

15
Parts of a Wave
  • Crest
  • Trough
  • Amplitude
  • Wavelength

16
  • If a train of freight cars, each 10 m long,
    rolls by you at the rate of 2 cars each second,
    what is the speed of the train?

17
  • Imagine that you fix your eyes at a stationary
    point on the surface of water and observe that
    two crests pass that stationary point each
    second. You also notice that the length of each
    wave is 3 meters. What is the speed of the wave
    in meters per second?

18
Wave Speed
  • Wave speed frequency x wavelength
  • In equation form v f?
  • ? Greek letter Lamda represents wavelength
  • Wave speed is measured in m/s

19
Constructive Interference
  • When the crest of one wave interferes with the
    crest of another, their individual effects add
    together.
  • The result of two crests interfering is a wave of
    increased amplitude.

20
Constructive Interference
  • When the trough of one wave interferes with the
    trough of another, their individual effects add
    together.
  • The result of two troughs interfering is a wave
    of increased amplitude.

21
Destructive Interference
  • When the crest of one wave interferes with the
    trough of another wave, their individual effects
    are reduced.
  • The high part (which is the crest) of one wave
    fills in the low part (which is the trough) of
    the other wave.

22
Destructive Interference
Sometimes a trough and crest will meet and
completely cancel out. Destructive interference
still occurs, but there is no resulting wave.
23
(No Transcript)
24
(No Transcript)
25
(No Transcript)
26
Do Now 3/13/09
  • Decide whether each labeled position in the
    following diagram is a position where
    constructive or destructive interference occurs.

27
Journal 3/13/09
  • 1.) What type of wave is associated with sound
    waves? Transverse or longitudinal?
  • 2.) Did Bill Nye help you understand certain
    concepts that you were unsure about before you
    watched the video? If so, what concepts?
  • 3.) List 5 things that you learned from the
    video.

28
Do Now 3/16/09
  • 1.) Explain what happens when a pulse is sent
    down a rope that is fixed at one end.
  • 2.) Explain what happens when a pulse is sent
    down a rope that is loosely tied at one end.
  • 3.) A tuning fork produces a sound with a
    frequency of 245 Hz. What would be the
    wavelength of this sound in water if the speed of
    sound in water is 1500 m/s?
  • 4.) What is the difference between a pulse wave
    and a periodic wave?
  • 5.) Draw the resultant wave of the two
    interfering waves on the board.

29
Standing Wave
  • An original wave (called the incidental wave) and
    the reflected wave form a standing wave.

30
Nodes and Antinodes
  • The parts of the wave that remain stationary are
    called nodes.
  • The positions on a standing wave with the largest
    amplitudes are called antinodes. Antinodes occur
    halfway between two nodes.

ANTINODES NODES
Write a Comment
User Comments (0)
About PowerShow.com