Vibrations and Waves

1
Vibrations and Waves

• Vibration a repeating back-and-forth motion
• A vibration cannot exist in an instant
• Wave a disturbance that repeats regularly in
  space and time
• A wave is a vibration in space and time
• Waves move energy from one position to another,
  not matter.
• Ex Light and sound

2
Parts of a Sine Wave

• Sine wave a pictorial representation of a wave.
• Crest the highest part of a sine wave
• Trough the lowest part of a sine wave
• Amplitude The distance from the midpoint to the
  crest or from the midpoint to the trough.
• The greatest vertical movement of the wave
• SI unit meters (m)

3
Sine Wave
4

• Wavelength the distance between successive
  identical parts of a sine wave.
• How far until a wave repeats itself
• Ex crest to crest, trough to trough
• SI unit meters (m)

5
Energy of a Wave

• The energy transferred from a vibrating source is
  carried by a disturbance in the medium, not by
  matter moving from one place to another.
• Waves move ENERGY, not matter
• Energy carried by a wave consist of KE and PE

6

• In a pendulum, the greatest KE is at the bottom
  of the swing
• This would be the middle (equilibrium line) of a
  sine wave
• The greatest PE is at the tallest points of the
  swing
• This would be the crest and trough of a sine wave
• The total energy of wave remains the same
• At the crests and troughs, there is the most PE
  and the least KE
• At the middle, there is the most KE and the least
  PE

7
Period and Frequency

• Period the time required to complete one cycle.
• The time for a wave to repeat itself
• SI Unit seconds (s)same as for time
• Period of a pendulum
• The time of a back and forth swing
• The period depends ONLY on
• the length of the pendulum
• A long pendulum has a longer period than a
  shorter pendulum.
• the acceleration due to gravity.

8
Check Your Understanding

• Which will have a greater period, a pendulum with
  a 5 kg mass on 1 m of string or a pendulum with a
  10 kg mass on 1 m of string?
• Neither! They both have the same period because
  they both have the same length. Mass has NO
  affect on the period of a pendulum.

9

• Frequency How frequently a vibration occurs.
• waves per second
• Unit Hertz (Hz) which means per second (1/s).
• If the frequency of a vibrating object is known,
  its period can be calculated and vice-versa.
• The frequency and period are inverses of each
  other.
• f 1/T
• T 1/f
• f frequency
• Measured in Hertz (Hz)
• T period
• Measured in seconds (s)

10
Check Your Understanding

• What is the frequency in vibrations per second of
  a 100 Hz wave?
• 100 Hz vibrates 100 times per second
• The Sears Building in Chicago sways back and
  forth at a frequency of about 0.1 Hz. What is
  the period of vibration?
• T? f 0.1 Hz
• T 1/f
• T 1/0.1 10 seconds

11
Transverse Waves

• Transverse wave a wave with a vibration at
  right angles to the direction the wave is
  traveling.
• The energy moves through the medium left to
  right, but the motion of the wave is up and down
• Makes an S shape wave
• Ex light waves, string instrument

12
(No Transcript)
13
Longitudinal Waves

• Longitudinal wave a wave in which the vibration
  is in the same direction as that which the wave
  is traveling.
• Both the energy motion and the movement of the
  wave are left to right
• Makes a pulse through the wave
• Ex sound waves, earthquake waves

14
(No Transcript)
15
Interference

• An interference pattern is formed by the
  overlapping of two or more waves that arrive in a
  region at the same time.
• There are 2 types of interference
• Constructive interference
• Destructive interference

16
Constructive Interference

• Constructive interference addition of two or
  more waves when wave crests overlap to produce a
  resulting wave of increased amplitude
• The amplitude of the two original crests are
  combined to add to the new amplitude
• Ex A noisy room (several sound waves adding at
  the same time)

17
Destructive Interference

• Destructive interference combination of waves
  where the crests of one wave overlap troughs of
  another, resulting in a wave of decreased
  amplitude.
• The amplitude of the original waves are
  subtracted because they are in opposite
  directions
• Ex anti-noise technology cancels out sound

18
Principle of Superposition

• Principle of Superposition the displacement of a
  medium caused by two or more waves is the
  algebraic sum of the displacements caused by the
  individual waves
• When two waves interfere with each other, the
  combined amplitude depends on the direction and
  height of the amplitude of the original wave.
• Ex subtracting amplitudes with destructive
  interference, adding amplitudes with constructive
  interference

19
(No Transcript)
20
Check Your Understanding

• Two waves reach the same place at the same time.
  One has an amplitude of 2 m up and the other has
  an amplitude of 3 m up. What type of
  interference is this?
• Constructive interference b/c both amplitudes are
  in the same direction.
• What is the new amplitude?
• Because they are up going up, you add the
  amplitudes.
• 2 3 5 m

21
Check Your Understanding

• Two waves reach the same place at the same time.
  One has an amplitude of 4 m up and the other has
  an amplitude of 4 m down. What type of
  interference is this?
• Destructive interference b/c the amplitudes are
  in opposite directions.
• What is the new amplitude?
• 4 4 0 m. There is no amplitude!

22
The Doppler Effect

• Doppler effect the change in frequency due to
  the motion of the source or the receiver.
• The greater the speed of the source, the greater
  the Doppler effect will be.
• Ex the shift in pitch of a siren as it drives
  past you

23
(No Transcript)
24
The Doppler Effect for Sound

• The pitch of sound is higher when the source
  moves toward you, and lower when the source moves
  away from you.
• Pitch is the same as frequency
• As a source (like a siren) and a receiver (like
  you) move closer together, the pitch increases
  b/c the frequency increases
• As a source (like a siren) and a receiver (like
  you) move away from each other, the pitch
  decreases b/c the frequency decreases

25

• http//www.colorado.edu/physics/2000/applets/doppl
  er2.html
• http//www.colorado.edu/physics/2000/applets/doppl
  er.html

26
The Doppler Effect for Light

• When the light source approaches, there is an
  increase in its measured frequency, and when it
  recedes, there is a decrease in its frequency.
• An increase in frequency is called a blue shift
  because it is shifted toward the high frequency,
  or blue, end of the color spectrum.
• A decrease in frequency is called a red shift
  because it is shifted toward the low-frequency,
  or red end, of the color spectrum.
• Blue shift ? object moves closer
• Red shift ? object moves away

27
Check Your Understanding

• When a source moves towards you, do you measure
  an increase or decrease in wave speed?
• Neither, you measure the change in FREQUENCY.
• Does the pitch increase or decrease?
• The pitch increases
• Does the frequency increase or decrease?
• Because the pitch increases, so does the frequency

28
Check Your Understanding

• On the news, if they say that the Doppler Radar
  is showing a blue shift for a storm front, is the
  storm moving towards you or away from you?
• Towards you. A blue shift is an increase in
  frequency, so the source (the storm) is moving
  towards the receiver (you).