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