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Objectives: After completion of this module, you should be able to:

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A mechanical wave is a physical disturbance in an elastic medium. ... Energy propagation via such a disturbance is known as mechanical wave motion. – PowerPoint PPT presentation

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Title: Objectives: After completion of this module, you should be able to:


1
Objectives After completion of this module, you
should be able to
  • Demonstrate your understanding of transverse and
    longitudinal waves.
  • Define, relate and apply the concepts of
    frequency, wavelength, and wave speed.
  • Solve problems involving mass, length, tension,
    and wave velocity for transverse waves.
  • Write and apply an expression for determining the
    characteristic frequencies for a vibrating string
    with fixed endpoints.

2
Mechanical Waves
A mechanical wave is a physical disturbance in an
elastic medium.
Consider a stone dropped into a lake.
Energy is transferred from stone to floating log,
but only the disturbance travels.
Actual motion of any individual water particle is
small.
Energy propagation via such a disturbance is
known as mechanical wave motion.
3
A Transverse Wave
In a transverse wave, the vibration of the
individual particles of the medium is
perpendicular to the direction of wave
propagation.
4
Longitudinal Waves
In a longitudinal wave, the vibration of the
individual particles is parallel to the direction
of wave propagation.
5
Wave speed in a string.
The wave speed v in a vibrating string is
determined by the tension F and the linear
density m, or mass per unit length.
L
m m/L
v speed of the transverse wave (m/s) F
tension on the string (N) m or m/L mass per
unit length (kg/m)
6
Example 1 A 5-g section of string has a length
of 2 M from the wall to the top of a pulley. A
200-g mass hangs at the end. What is the speed of
a wave in this string?
F (0.20 kg)(9.8 m/s2) 1.96 N
v 28.0 m/s
Note Be careful to use consistent units. The
tension F must be in newtons, the mass m in
kilograms, and the length L in meters.
7
Periodic Wave Motion
A vibrating metal plate produces a transverse
continuous wave as shown.
For one complete vibration, the wave moves a
distance of one wavelength l as illustrated.
8
Velocity and Wave Frequency.
The period T is the time to move a distance of
one wavelength. Therefore, the wave speed is
The frequency f is in s-1 or hertz (Hz).
The velocity of any wave is the product of the
frequency and the wavelength
9
Production of a Longitudinal Wave
  • An oscillating pendulum produces condensations
    and rarefactions that travel down the spring.
  • The wave length l is the distance between
    adjacent condensations or rarefactions.

10
Velocity, Wavelength, Speed
Wave equation
11
The Superposition Principle
  • When two or more waves (blue and green) exist in
    the same medium, each wave moves as though the
    other were absent.
  • The resultant displacement of these waves at any
    point is the algebraic sum (yellow) wave of the
    two displacements.

Constructive Interference
Destructive Interference
12
Formation of a Standing Wave
Incident and reflected waves traveling in
opposite directions produce nodes N and antinodes
A.
The distance between alternate nodes or
anti-nodes is one wavelength.
13
Possible Wavelengths for Standing Waves
Fundamental, n 1
1st overtone, n 2
2nd overtone, n 3
3rd overtone, n 4
n harmonics
14
Possible Frequencies f v/l
Fundamental, n 1
1st overtone, n 2
2nd overtone, n 3
3rd overtone, n 4
n harmonics
15
Characteristic Frequencies
Now, for a string under tension, we have
Characteristic frequencies
16
Example 2. A 9-g steel wire is 2 m long and is
under a tension of 400 N. If the string vibrates
in three loops, what is the frequency of the wave?
For three loops n 3
Third harmonic 2nd overtone
f3 224 Hz
17
Summary for Wave Motion
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