Waves

1
Waves

• Physics H

2
Pendulum

• A pendulum is simply a mass (bob) suspended from
  a string that can swing back and forth
• The time it takes for the pendulum to swing back
  and forth is called the period.
• Period depends on length of the pendulum, not on
  weight suspended.
• The back and forth motion is called simple
  harmonic motion (SHM)
• Produces a sine curve

3

• The restoring force of a pendulum is a component
  of the bobs weight
• x-component pushes the bob toward equilibrium
• At small angles, a pendulum follows SHM
• At large angles this breaks down
• Potential energy increases as displacement
  increases
• Cons of energy still applies PE KE const.

4
Hookes Law

• Hookes Law
• Felastic -kx
• k spring constant
• x displacement
• - force is always opposite direction from
  displacement
• See Figure 12-1
• A stretched or compressed spring has elastic
  potential energy

• The following holds true for a pendulum or a
  spring
• At the equilibrium point, v is a max
• At max displacement, force and a are max
• In SHM restoring force is proportional to
  displacement

5
Sample Problem 12A

• If a mass of .55kg attached to a vertical spring
  stretches the spring 2.0cm from its equilibrium
  position, what is the spring constant?
• Not accelerating so Nnet 0
• Fnet 0 Felastic - FW

6

• -kx mg 0
• Rearange k -(mg)/x
• k -(.55kg)(9.8m/s2)/(-.02m)
• k 270 N/m

7
Pendulum Mass-Spring

• The period of a simple pendulum can be calculated
  with
• period 2? x square root of length / gravity

• Period of a mass spring system in SHM
• period 2? x square root of mass / spring
  constant

8
Ex

• When a mass of 25g is attached to a certain
  spring, it makes 20 complete vibrations in 4.0s.
  What is the spring constant?
• Calculate period first
• 4.0s/20vibrations .2s / vibration
• Now use the formula

9

• .2s 2?v(.025kg/k)
• .1s/ ? v(.025kg/k) square both sides
• .00101s2 .025kg / k
• k 25 N/m

10
Sample Problem 12B

• You need to know the height of a tower, but
  darkness obscures the ceiling. You note that a
  pendulum extending from the ceiling almost
  touches the floor and that its period is 12 s.
  How tall is the tower?

11
Sample Problem 12C

• The body of a 1275 kg car is supported on a frame
  by four springs. Two people riding in the car
  have a combined mass of 153 kg. When driven over
  a pothole in the road, the frame vibrates with a
  period of 0.840 s. For the first few seconds, the
  vibration approximates SHM. Find the spring
  constant of a single spring.

12

• Homework
• 12A-C odd

13
Wave Motion

• Mechanical waves travel by molecules vibrating
  back and forth or up and down.
• Sound, ocean wave
• They have to travel through a medium
• Water, air
• Pulse single traveling wave

14
Wave Types

• Transverse Wave - Motion of the wave is at right
  angles to the direction the wave is moving.

• Longitudinal Wave - Motion of the wave is in the
  same direction as the direction the wave is
  moving.

15
(No Transcript)
16
Wave Description

• Waves are made up of several parts
• Crests - high points
• Troughs - low points
• Amplitude - distance from the midpoint to the
  crest or trough

• Wavelength - distance form the top of one crest
  to the top of the next.
• Frequency - How often a vibration occurs.
• Period - amount of time for 1 cycle

17
Wave
18
Frequency

• Frequency measures the number of times a wave
  oscillates in a given time (second)
• Frequency is measured in hertz
• 1 cycle per second 1 hertz
• frequency 1/period
• period 1/frequency

19
Wave Speed

• Wave speed depends on what type of medium it is
  traveling through
• The speed of a wave is dependant upon 2 things,
  wavelength and frequency
• Wave speed wavelength x frequency
• v ?f

20
Examples

• The Sears tower swings back and forth at a
  frequency of .1Hz what is its period?
• What is the wavelength of a 170Hz sound wave when
  the speed of sound in air is 340m/s?

• Frequency 1/period
• .1Hz 1/period
• Period 10s
• v ?f
• 340m/s ?(170Hz)
• ? 2.0m

21
Sample Problem 12D

• The piano string tuned to middle C vibrates with
  a frequency of 264 Hz. Assuming the speed of
  sound in air is 343 m/s, find the wavelength of
  the sound waves produced by the string.

22
Interference

• Occurs every time two waves overlap
• Constructive - When crests of two waves overlap,
  it results in increased amplitude. The waves are
  said to be in phase
• Destructive - When the crest of one wave overlaps
  with the trough of another wave, they cancel each
  other out. The waves are said to be out of phase
  with each other.

23

• .

24
Reflection

• When ever a wave transfers from one medium to
  another, part of the wave reflects and part of
  the waves energy continues on.
• At a free boundary, waves are reflected.
• At a fixed boundary, waves are reflected and
  inverted.

25
Standing Waves

• If a string attached to a wall vibrates at
  exactly the right frequency, it can produce a
  standing wave.
• Standing Wave- A wave pattern that does not move
  along the string.
• Node There is no motion on the string
• Antinode midway between the nodes, vibrations
  have the largest amplitude

26
Review

• What are the two types of interference?
• How fast is a wave with a wavelength of 3m and a
  frequency of 212Hz moving?
• Describe the two types of waves.

• If a wave has a period of .2s, what is its
  frequency?
• A radio station has a frequency of 101 MHz, what
  is the period of its wave?
• What are the two points of importance on a
  standing wave?

27
Chapter 12 Review

• p. 469 8-9
• p. 470 19-22 and 35
• p. 471 36