 Chapter 13 part II
Types of Waves
Longitudinal Wave
Transverse Wave
Speed of Wave
Reflection of Wave
Superposition of Waves
 Wave pulse is a disturbance that carries energy through a medium or space
Medium is disturbed  energy is imparted to it  some particles start vibrating
 Medium matter that wave/pulse is traveling through: solid, gas, liquid, plasma
 Wave Motion
 A periodic wave is a regular rhythmic disturbance in both time and space that propagates from one
place to another
 All waves transport energy
 Matter is not transported, particles just vibrate around equilibrium position
 A periodic wave is caused by a disturbance or vibration from an oscillating source
If diving source maintains constant amplitude  simple harmonic motion (sinusoidal form)
 Types of Waves:
Mechanical waves
 Require a medium
 Require some physical connection between which adjacent portions of the medium influence each other
Electromagnetic waves
 Do not require a medium
 Travel through a vacuum at a speed of 3.0 x 108 m/s
 Types of Mechanical Waves
Transverse
Longitudinal
 Transverse Wave
 Particles of the medium that are disturbed move perpendicularly to the direction of propagation of the
wave
 Particles of matter vibrate around equilibrium (rest) position
 Particles of matter do not travel:
3/23/2016
Document1
1
 Matter is not transported
 Longitudinal Wave
 Individual particles oscillate in the same direction (parallel) as the direction of propagation of the wave
 Surface wave is a combination of transverse and longitudinal wave
 Surface wave (water wave)
 Parts of a Wave - Transverse wave:
 Crest: The highest part of the disturbance on a wave
 Trough: The lowest part of the disturbance on a wave
 Parts of a Wave - Longitudinal Wave:
 Compression – compressed part (high density area)
 Rarefaction – stretched part (low density area)
 A longitudinal wave can also be represented as a sine curve
 Compressions correspond to crests and rarefactions (stretches) correspond to troughs
 Wave Characteristics
 Amplitude, A is the maximum displacement of string above the equilibrium position or the "height" of
the wave
 Amplitude measures the energy in the wave
 Wavelength, λ the length of one wave. It is measured by taking the distance from one point on
a wave to the same point on the next wave (for example, the distance from one wave crest to
the next)
 Period T: the time interval in which the wave motion begins to repeat itself
 Frequency f: the number of waves that occur in a unit of time f = 1/T
 Frequency of a source and the wave it produces are the same
 SI unit: Hz (hertz) 1 Hz = 1 s-1 (cycles per second)
 a - ……..
b - ……..
c - ……..
d - …….
 The frequency, wavelength, and velocity are related to each other
 Speed of a wave v: is the velocity at which wave crests move
 This is a general equation that can be applied to many types of waves
 THE WAVE SPEED DOES NOT DEPEND ON THE AMPLITUDE
 THE WAVE SPEED DOES NOT DEPEND ON FREQUENCY, or WAVELENGTH
 The speed of a wave DEPENDS on the MEDIUM it travels through
3/23/2016
Document1
2
 ex1
A wave has a speed of 20. m/s. The frequency of it is 25 Hz.
(a) Find the wavelength for this wave.
(b) Find the period for this wave.
 ex2
A person on a pier observes a set of incoming waves that have sinusoidal form with a distance of 1.6 m between
the crests. If a wave laps against the pier every 4.0 s, what are the frequency and the speed of the waves?
 Speed of a Wave on a String
 The speed depends on the properties of the medium through which the disturbance travels

The speed of a wave in a stretched string depends on tension in the string FT, and the string’s mass per
unit length m/L
 The greater the m/L, the more inertia the string has and the more slowly the wave will propagate (the
heavier the rope, the slower the speed under same tension)
 ex3
A 5.0 m length of rope, with the mass of 0.52 kg, is pulled with the tension of 46 N. Find the speed of the wave
on the rope.
 ex4
A 12 m rope is pulled tight with a tension of 92 N. When one end of the rope is given a “thunk” it takes 0.45 s for
the disturbance to propagate to the other end. What is the mass of the rope?
If the tension in the rope is doubled, how long will it take for the thunk to travel from one end to the other?
 ex5
A rope of length L and mass M hangs from a ceiling. If the bottom of the rope is given a gentle wiggle, a wave
will travel to the top of the rope. As the wave travels upward, does its speed (a) increase,
(b) decrease, or (c)
stay the same?
 Reflection is bouncing back of a wave as it meets a boundary of two media
 When a traveling wave pulse is reflected from a fixed end, the reflected wave pulse is on the opposite
side → inverted
 When a traveling wave pulse is reflected from a free end, the reflected pulse is on the same side
 In Phase/Opposite Phase
 Two waves have the same frequency
 Waves a and b are in phase
 Waves a and b are 180° out of phase – in opposite phase
 Pulses are in phase:
Pulses are in opposite phase:
 Waves Obey Superposition Principle
3/23/2016
Document1
3
 Two traveling waves can meet and pass through each other without being destroyed or even altered
 If two or more traveling waves are moving through a medium, the resulting wave is sum of the
displacements of the individual waves point by point
The result of the superposition of two or more waves is called interference
 Two traveling waves pass through each other without being destroyed or changed
 The combined wave (c) has greater amplitude – constructive interference
 Two pulses are traveling in opposite directions
 The net amplitude when they overlap is the sum of the amplitudes of the pulses
 Note that the pulses are unchanged after the interference
 When blue and green waves combine, the combined wave (red) has a greater amplitude:
Constructive Interference
 When blue and green waves combine, the waveforms cancel - the combined wave (red) has smaller
amplitude:
Destructive Interference
 Two waves, a and b, have the same amplitude and frequency
 When the two waves combine, the waveforms cancel (c) – complete destructive interference
 Two pulses are traveling in opposite directions
 For the net amplitude when they overlap you subtract the amplitudes of the pulses
 Note that the pulses are unchanged after the interference
 Standing Wave
 When a traveling wave reflects back on itself, the incident wave and reflected wave interfere
 With exactly the right frequency, the wave will appear to stand still
This is called a standing wave
 Node occurs where the wave and the reflected have the same size amplitude, but they are in opposite
sides
 Net displacement at that point is zero
 Destructive interference
 The distance between two nodes is ½ λ
 Antinode occurs where the wave and the reflected have the same size amplitude
 Net displacement has maximum amplitude at that point
 Constructive interference
 The distance between two antinodes is ½ λ
 Exercise
3/23/2016
Document1
4
1. How many standing waves are on each picture?
2. If the length of the string is 6 meters, what is the wavelength of the wave on each picture?
 Standing Waves on a String
 Nodes must occur at the ends of the string because these points are fixed
 Standing Waves on a String
 The lowest frequency of vibration (b) is called the fundamental frequency
 ƒ1, ƒ2, ƒ3 form a harmonic series
 ƒ1 is the fundamental and also the first harmonic
 ƒ2 is the second harmonic
 ƒ3 is the third harmonic
 Standing Waves on a String, cont.
 In terms of musical intervals...
The first harmonic is the fundamental.
The second harmonic is an octave above.
The fourth harmonic is two octaves above the fundamental.
Fundamental
2nd Harmonic
3rd Harmonic
(1st Harmonic)
 Waves in the string that are not in the harmonic series are quickly damped out
 When the string is disturbed, it “selects” the standing wave frequencies
 ex6
One of the harmonics on a 1.30 m long string has a frequency of 15.60 Hz. The next higher harmonic has a
frequency of 23.40 Hz. Find (a) the fundamental frequency and (b) the speed of the waves on this spring?
 Intensity of Waves
 Waves transport energy from one place to another
 Each particle in a sinusoidal wave with frequency f moves in SHM as a wave passes, and has energy
E = ½ k A2, where A is the amplitude
 The intensity of a wave is the rate at which the energy flows through a unit area (perpendicular to the
direction of the wave)
 Units: W/m2
 P is the power (energy per time)
 Intensity I is proportional to the wave amplitude squared
I ~ A2
 Spherical Waves
3/23/2016
Document1
5
 A spherical wave propagates radially outward from the oscillating point source
 Energy propagates equally in all directions
I ~ 1/r2:
 Intensity of a Point Source
 Since the intensity varies as 1/r2 (I ~ 1/r2), this is an inverse square relationship
 To compare intensities at two locations, the inverse square relationship can be used
 Representations of Waves
 Wave fronts are the concentric arcs
 The distance between successive wave fronts is the wavelength
 Rays are the radial lines pointing out from the source and perpendicular to the wave fronts
 Plane Wave
 Far away from the source, the wave fronts are nearly parallel planes
 The rays are nearly parallel lines
 A small segment of the wave front is approximately a plane wave
 Waves at Boundaries: Refraction
 A wave entering another medium at an angle will change direction
 Reason for refraction: speed of a wave is different in different media
 The speed of the wave in shallow water is smaller than in deeper water
 The slower wave in the shallow water has a smaller wavelength (λ2)
 Frequency (f) will not change
 ex
A wave travels from one medium to another, and the wavelength decreases.
What happens to the speed?
What happens to the frequency?
 ex
A wave travels from one medium to another, and the speed increases.
What happens to the frequency?
What happens to the wavelength?
 Diffraction bending of a wave as it passes around an edge or through an opening
Bending is greatest when the size of opening is similar to the wavelength
3/23/2016
Document1
6