# PH300 Waves 2013 ```PH300 Waves
The Great Wave off Kanagawa Katsushika Hokusai
2013
What is a wave?
●
Pulse or Oscillation that Propagates through
Media
●
What is transferred?
●
What sorts of Media?
Harmonic Waves
8/23/2013
8/23/2013
Exercise
Consider a mechanical wave y(x,t)= 0.2cos(π/8(x-32t))
where x is measured in meters and t is measured in seconds
Determine:
a.
b.
c.
d.
e.
f.
g.
Amplitude
Wave Number
Wavelength
Speed
Frequency
Period
Angular Frequency
A=0.2 m
k=π/8 m-1
λ=16 m
v=32 m/s
ν=2 Hz
T=0.5 s
ω=4π s-1
Exercise
Consider a mechanical wave y(x,t)= 0.2cos(π/8(x-32t))
where x is measured in meters and t is measured in seconds
Determine:
a.
b.
c.
d.
e.
f.
g.
Amplitude
Wave Number
Wavelength
Speed
Frequency
Period
Angular Frequency
A=0.2 m
k=π/8 m-1
λ=16 m
v=32 m/s
ν=2 Hz
T=0.5 s
ω=4π s-1
Harmonic Waves
•
Alternate Representation
Assuming
y(x,t)=Acos k(x+vt)
can obtain
y(x,t)=Acos(kx+ωt)
Or the equivalent
y(x,t)=Acos 2π(x/λ+t/T)
8/23/2013
Velocity and Acceleration
8/23/2013
Problem
In the open sea, a tsunami usually has
an amplitude less than 40 cm and a
wavelength longer than 80 km.
Assume that the speed of the tsunami
is 740 km/h.
What are the approximate maximum
vertical velocity and acceleration that
such a tsunami will give to a ship
floating on the water? Will the crew of
the ship notice the passing tsunami?
8/23/2013
Velocity in y
vy~ π/500 m/s
Acceleration= vy/A
= (pi/500) (1/0.4) m/s2
= 0.0001 m/s2
g=10 m/s2
8/23/2013
Depth of Ocean
Monitor
Open Ocean,
600 km SE of Tokyo
Δy 1.1 m