Saturday Sept 12th: Spring tides and sneaker waves.

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Saturday Sept 12th: Spring tides and sneaker waves

Transcript of Saturday Sept 12th: Spring tides and sneaker waves.

Page 1: Saturday Sept 12th: Spring tides and sneaker waves.

Saturday Sept 12th:Spring tides

and sneaker waves

Page 2: Saturday Sept 12th: Spring tides and sneaker waves.

x

y

( )y f x

y mx b

Functionsrelation

linear function

function

Page 3: Saturday Sept 12th: Spring tides and sneaker waves.

x

y

( )y f x

y mx b

Functionsrelation

linear function

function

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Sine and cosine functions, oscillation period = 2π

2π0

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1

cos0

/2

/2

sin

The unit circle

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The addition rule

sin( ) sin( ) 2sin cos2 2

( ) ( )a b a ba b

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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

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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 2

2 2f f f f

f 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

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The Seventh WaveA product of sine and cosine with different frequencies

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Beats

1 2 1 21 2sin(2 ) sin(2 ) 2sin 2 cos 2

2 2f f f f

f 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

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WAVES ENVELOPE

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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

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Swell and sneaker waveson the

Oregon Coast

Log carried by sneaker waveApril 2007, Cannon Beach OR

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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| | 0.020249.5

1/ 49.5Sneaker wave interval = 59.91/

m

b

b

m

f s f ss s

f ff s

s

f f f ss

f ssf

Mean period = 9.9s

Beat period = 49.5s

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Tides

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Lunar tides

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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

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Solar tides

Earth orbits Sun every 365 days

Tidal frequency = 2/24hrs-1/365days =1/12.0hrs

Tidal period = 12.0 hrs

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Spring tide

OR

Constructive interferenceTidal range is HIGH

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Neap tide

Destructive interferenceTidal range is LOW

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Fri 18Wed16Mon 14Sat 12 Sun 20Sun 13 Tue 15 Thu 17 Sat 19

Tides at Newport, Sept 12-20 2009

Spring tides

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