Waves – Topic 4
Chapters 13, 14, 25, 26
Traveling Waves
 Wave
Motion: Disturbance which
travels in a medium transferring
energy and momentum.
– No Transfer of Mass!!!
 Two
Classifications
– Mechanical Waves (require a medium)
 Ex:
sound, water, Earth Quakes
– Electromagnetic Waves (travel in vacuum)
 Ex:
light, microwaves – see chart
Speed depends on Medium
 Sound
depends on Temp & Pressure
 Strings/Springs
depends on tension
and linear mass density
 Electromagnetic
waves all travel the
same speed in a vacuum.
3.0 x 108 m/s.
Speed depends on Medium
 Velocity
of sound at STP is 330 m/s.
(Standard Pressure and Temp.)
STP - 1 atmosphere and 0˚Celsius.
 +/ At
0.6 m/s for every 1˚C +/-
room temp. (22 degrees)
v ≈ 343 m/s
Table 14-1
Speed of Sound in Various Materials
Material
Speed (m/s)
Aluminum
6420
Granite
6000
Steel
5960
Pyrex glass
5640
Copper
5010
Plastic
2680
Fresh water (20 ºC)
1482
Fresh water (0 ºC)
1402
Hydrogen (0 ºC)
1284
Helium (0 ºC)
965
Air (20 ºC)
343
Air (0 ºC)
331
Reflection of Pulses
 The
pulse becomes inverted upon
reflecting off the fixed end.
Reflection at boundary

The transmitted pulse is not inverted and
maintains the same phase. The reflected
pulse is is also not inverted.
Sound
is
Longitudinal Wave
Displacement of the particle is parallel to the
propagation or direction of wave travel.
Light
is
Transverse Wave
Displacement of the particle is at right angles to
the propagation or direction of wave travel.
Conceptual Checkpoint 14-2
How far away is the lightning?
Echo Problem
 You
shout at a canyon wall and here
your echo 2.4 seconds after you
shout. How far away is the canyon
wall? Assume v = 343 m/s
 d = vt
 d=
343m/s (1.2 sec)
 d= 412 m to the wall.
half the time
Wishing Well – Making a Splash!

How long after dropping the stone
will the boy hear the splash?
Making a Splash - Solution
 First
calculate the time for the stone
to reach the water. d=vit + ½gt2
 t= 1.22 sec
 Then
calculate the time for the sound
wave to travel back up. d=vt
 t= 0.02 sec
 Add
the two times. t= 1.24 sec
Periodic Waves - Terminology

Frequency –
The number of vibrations or oscillations
per unit time.
Unit Hertz (Hz) – derived.

Period –

Amplitude –

Wavelength –
Time required for one complete cycle or to
move the linear distance of one wavelength.
Unit second (s) – Fundamental.
The maximum displacement of a
particle of the medium from the rest position.
Unit meter (m)– Fundamental.
The distance traveled by one wave in
one period. The distance between two consecutive points in
phase.
Unit Meter (m) – Fundamental.
Traveling Wave Characteristics




Frequency is the reciprocal of Period
f = 1/T or T = 1/f
Determine the frequency of a wave with a
period of 0.01667 sec.
f =1/T , f = 1/ (0.01667 sec) = 60 Hz
What happens to the period of a wave as
its frequency increases?
Wave Speed – wave equation




Wave equation can be derived from the
kinematics equation
v = d/t
If d=λ(wavelength) and t=T(period), then
v= λ/T
Since f = 1/T, then
v=fλ
Wave Speed
A
sound wave in a steel rail has a
frequency of 620 Hz and a
wavelength of 10.5 m. what is the
speed of sound in steel?
 v=f λ
 v= 620hz (10.5 m)
 v= 6510 m/s
Periodic Wave Phenomena
 Huygens
Principle: - Wavelets!
– This principle uses the wave concepts to
explain periodic wave phenomena.
 Reflection
 Refraction
 Diffraction
 Wave-fronts
 Sun
Ripple
Reflection

Law of Reflection
– The angle of
incidence equals
the angle of
reflection. Θi = θr

The incident and
reflected rays lie in
the same plane
with the normal.
Refraction

Sudden change in direction of a wave as
it changes speed.
– It must enter obliquely to change direction!
Refraction

In both cases the speed of the wave has
decreased. This is indicated by the
decrease in wavelength!
Refraction of Sound


When a wave slows down it bends closer to the
normal.
When a wave speed up it bends away from the
normal.
Diffraction
The bending or
spreading out
around the edges
of a barrier or
obstruction.
 Does the speed
change?
 No! You can see
the wavelength is
constant.

Diffraction

The extent of the
diffraction depends
on the ratio of the
wavelength to the
opening of the
hole.
Diffraction ~ λ/D
 Tsunami Waves

Interference
Constructive Interference
Destructive Interference
Waves DO NOT bounce! Energy passes through.
Superposition
 The
Algebraic sum of the amplitudes
of two or more waves which form
interference.
 Waves which arrive in phase form
constructive interference.
 Waves which meet out of phase form
destructive interference.
Standing or Stationary Waves
 Conditions
need:
– Same Amplitude
– Same frequency
– Opposite Directions
 Caused
by both Constructive and
Destructive interference.
– Nodes – Destructive
– Antinodes - Constructive
Harmonics
 Vibrating
strings or pipes form
Stationary wave patterns each
pattern refers to a different
Harmonic.
Beats
 When
two frequencies are very close
they interfere creating a beat sound.
 Beat frequency = F1 –F2
Figure 14-22
Interference with Two Sources
Interference
Path Diff = n λ, Constructive Int.
Doppler Effect
EEE OOOOOOO

EE

Movement toward or decreasing distance produced a
higher frequency.
Figure 14-15
The Doppler Effect: A Moving Observer
Doppler Effect
What happens when the
moving source reaches or
exceeds the speed of the
wave?
The Doppler Effect and
Sonic Booms
Plane-Mach1
Resonance
 Is
it Live or is it Memorex –viewed
under a strobe light
 An
Incredibly Irritating
Resonance Demonstration
 Resonating
Wave – Match the λ
Tacoma Narrows Bridge


On November 7, 1940, at approximately
11:00 AM, the first Tacoma Narrows
suspension bridge collapsed due to windinduced vibrations.
Situated on the Tacoma Narrows in Puget
Sound, near the city of Tacoma,
Washington, the bridge had only been
open for traffic a few months.