Saturday Sept 12th:Spring tides
and sneaker waves
x
y
( )y f x
y mx b
Functionsrelation
linear function
function
x
y
( )y f x
y mx b
Functionsrelation
linear function
function
Sine and cosine functions, oscillation period = 2π
2π0
1
cos0
/2
/2
sin
The unit circle
The addition rulesin( ) sin( ) 2sin cos2 2( ) ( )a b a ba b
Wave superposition0 0( ) sin 2 , or ( ) sin 2( ) ( )th t h ft h t h T
f = frequency T=period=1/f
1 wave:
0 1 0 2( ) sin 2 sin 2( ) ( )h t h f t h f t 2 waves:
ho = amplitude
same amplitude (for simplicity) but different frequency
Wave superposition0 0( ) sin 2 , or ( ) sin 2( ) ( )th t h ft h t h T
f = frequency T=period=1/f
1 22 ; 2a f t b f t
1 2 1 21 2sin(2 ) sin(2 ) 2sin 2 cos 22 2
f f f ff t f t t t
sin( ) sin( ) 2sin cos2 2( ) ( )a b a ba b Addition rule:
1 wave:
0 1 0 2( ) sin 2 sin 2( ) ( )h t h f t h f t 2 waves:
ho = amplitude
The Seventh WaveA product of sine and cosine with different frequencies
Beats
1 2 1 21 2sin(2 ) sin(2 ) 2sin 2 cos 22 2
f f f ff t f t t t
1 22
f f= mean frequency fm
1 2|2
|f f= half-beat frequency fb /2
wave envelope
1 2IF , then mbf f f f
WAVES ENVELOPE
Beats1 2
2f f
= mean frequency fm
1 2IF , then mbf f f f
1 21 2
| 2|2 ||f f f f = beat frequency fb
Swell and sneaker waveson the
Oregon Coast
Log carried by sneaker waveApril 2007, Cannon Beach OR
Sum of 9-second swell and 11-second swell
1 11 2
11 2
11 2
1 10.111 0.0919 11
10.1012 9.9
1| | 0.0202 49.5
1/ 49.5Sneaker wave interval = 59.91/
m
b
bm
f s f ss s
f ff s s
f f f s s
f ssf
Mean period = 9.9s
Beat period = 49.5s
Tides
Lunar tides
Lunar tides
2 bulges2 high tides per day
Moon orbits Earth every 30 days
Tidal frequency = 2/24hrs-1/30days =1/12.4hrs
Tidal period = 12.4 hrs
Solar tides
Earth orbits Sun every 365 days
Tidal frequency = 2/24hrs-1/365days =1/12.0hrs
Tidal period = 12.0 hrs
Spring tide
OR
Constructive interferenceTidal range is HIGH
Neap tide
Destructive interferenceTidal range is LOW
Fri 18Wed16Mon 14Sat 12 Sun 20Sun 13 Tue 15 Thu 17 Sat 19
Tides at Newport, Sept 12-20 2009
Spring tides
Recommended