Download Module 2, Lecture 3 • 1D • 2D • 3D A wave is a

Module 2, Lecture 3
Waves: Basic definitions
Waves
You are in a boat out on the ocean watching the waves go
by. To fully describe the waves, you need three things:
A wave is a ___________ that propagates
in a certain direction with a certain speed.
1.
Direction of Motion
2.
• 1D
• 2D
• 3D
3.
Physical medium
-Waves in water
-Waves in elastic bodies
-Sound
Empty space (a vacuum)
Electromagnetic waves
EF 152 Lecture 2-3
1
Examples: Tsunami and Ultrasound
•
T, period– Time for one wavelength to pass
•
ω, angular frequency–
•
v, wave velocity – How fast the wave is moving
•
k, wave number – 2 /
EF 152 Lecture 2-3
2
How many wavelengths are shown?
2
Some Types of Waves
Transverse
Satellite photos of the December 26, 2004 tsunami
showed a spacing of wave crests of 800 km and a
period between the waves of 1 hour.
Find the speed of the waves in km/hr.
Longitudinal
In a typical ultrasound, waves travel through body
tissue with a speed of 1500 m/s. For a good detailed
image, the wavelength should be no more than 1 mm.
Find the frequency required for a good scan.
Surface Waves
(circular)
EF 152 Lecture 2-3
1/
3
EF 152 Lecture 2-3
= tension
= mass per
unit length
= modulus of
elasticity
= mass
density
Units of E?
4
Example: Underground cables
The Wave Equation
To determine the location of a break in an underground
cable, the cable can be hit with an instrumented
hammer to generate a longitudinal wave. Find the
location of a break in the cable if it takes 0.038 seconds
for the wave to travel down and back.
Periodic in both
space and time
y  x, t   A coskx  t 
E = 29x106 psi
γ = 490 lb/ft3
Speed of the wave
v
dx 
2f
 
 f
dt k 2 / 
This is for wave traveling to right (forward). For wave moving to the
left, the argument is (kx+ωt)
y  x, t 
Motion of
vy 

a particle:
t
Distance?
ay 
EF 152 Lecture 2-3
5
Power and Energy in Waves
Waves transfer energy, without the
transfer of mass.
E  2 2 vtf 2 A2
Average power transmitted:
P P 
Wave Intensity
E
 2 2 vf 2 A2
t
Instantaneous power:
P  4 2 vf 2 A2 cos 2 kx  t 
I
1
r2
6
A tornado warning siren can produce a sound of intensity
I1= 0.25 W/m2 at 15 m away.
A) What is the intensity at 30 m away?
P
P

Surface Area 4r 2
I
vwave vs. vparticle
EF 152 Lecture 2-3
Example: Tornado Warning Siren
Average power transferred
across unit area perpendicular
to energy flow.
I
 2 y  x, t 

t 2
Particle follows ____________________
1.) 2*I1
2.) 4*I1
3.) I1/2
4.) I1/4
B) What power is required to run the siren?
I 2 r12

I1 r22
C) To hear the siren, it should have a greater intensity
than normal conversation, which is 1x10-6 W/m2. How
far away can you hear the siren?
2 2 vf 2 A2
 2 2 vf 2 A2
Surface Area
Ocean Waves: 1.5 m amplitude, 8 sec period
Power generated is 70.6kW/m
At 20% efficiency, 0.08 m crest length needed per house
EF 152 Lecture 2-3
8
EF 152 Lecture 2-3
9