Physics 110 Lecture 31 from Chapter 13 Sections 7 to 11

1
Physics 110 Lecture 31 from Chapter 13
Sections 7 to 11

• Waves

2
Homework Assignment 31

• Conceptual Questions
• Chapter 13, Question 13
• Problems
• Chapter 13, Problem 41 on page 454
• Chapter 13, Problem 43 on page 454
• Chapter 13, Problem 52 on page 454

3
Wave Motion

• A wave is the motion of a disturbance
• Mechanical waves require
• 1) Some source of disturbance
• 2) A medium that can be disturbed
• 3) Some physical connection between or mechanism
  though which adjacent portions of the medium
  influence each other
• All waves carry energy and momentum

4
Types of Waves Traveling Waves

• Flip one end of a long rope that is under tension
  and fixed at one end
• The pulse travels to the right with a definite
  speed
• A disturbance of this type is called a traveling
  wave

5
Types of Waves Transverse

• In a transverse wave, each element that is
  disturbed moves in a direction perpendicular to
  the wave motion

6
Types of Waves Longitudinal

• In a longitudinal wave, the elements of the
  medium undergo displacements parallel to the
  motion of the wave
• A longitudinal wave is also called a compression
  wave

7
Waveform A Picture of a Wave

• The brown curve is a snapshot of the wave at
  some instant in time
• The blue curve is later in time
• The high points are crests of the wave
• The low points are troughs of the wave

8
Wave form
A is the amplitude
? is the wavelength
f is the frequency -the number of waves that
pass by a point each time period.
vf ?
v is the wave speed
9
Example Problem 1

• A wave traveling i the positive
• x-direction has a frequency of 25 Hz as shown.
• Find
• a) amplitude
• b) wavelength
• c) period
• d) speed of the wave

10
Example Problem 1

• Given frequency f 25 cyc/s
• a) amplitude
• A 18cm/2
• 9 cm
• b) wavelength
• ? 2x10 cm
• 20 cm
• c) period
• T 1/f 1/(25 cyc/s)
• 0.04 s
• d) speed of the wave
• v ? f 20 cm x 25 cyc/s
• 500 cm/s

11
What determines wave speed?

• Wave speed is determined by how the elastic
  nature and the inertia of the medium interact.
• For transverse waves velocity in a stretched
  string or wire is given by
• For longitudinal waves the velocity is In a
  long solid rod In a liquid or gas

Ft is tension in the wire µ is mass per unit
length
where E is Elastic modulus, ? is density, and B
is Bulk modulus
12
Example Problem

• A sailor strikes the side of a ship just below
  the surface of the sea. He hears an echo of the
  wave reflected from the ocean floor directly
  below 2.1 s later. How deep is the ocean?
• ?sea_water1025 kg/m3
• Bwater 2 x 109 Pa

13
Example Problem

• ?sea_water1025 kg/m3
• Bwater 2 x 109 Pa

14
Longitudinal Wave Represented as a Sine Curve

• A longitudinal wave can also be represented as a
  sine curve
• Compressions correspond to crests and stretches
  correspond to troughs
• Also called density waves or pressure waves

15
Description of a Wave

• A steady stream of pulses on a very long string
  produces a continuous wave
• The blade oscillates in simple harmonic motion
• Each small segment of the string, such as P,
  oscillates with simple harmonic motion

16
Amplitude and Wavelength

• Amplitude is the maximum displacement of string
  above the equilibrium position
• Wavelength, ?, is the distance between two
  successive points that behave identically

17
Interference of Waves

• Two traveling waves can meet and pass through
  each other without being destroyed or even
  altered
• Waves obey the Superposition Principle
• If two or more traveling waves are moving through
  a medium, the resulting wave is found by adding
  together the displacements of the individual
  waves point by point
• Actually only true for waves with small amplitudes