Chapter 1

Question 1

…………………. support many wavelike motions

Answer 1

The governing equations

Question 2

waves are broadly defined as

Answer 2

oscillations of the dependent variables

Question 3

Some of the waves supported by the equations are:

Answer 3

• External (surface) gravity waves
• Internal gravity waves
• Inertia-gravity waves
• Acoustic waves (including Lamb waves)
• Rossby waves
• Kelvin waves
• Kelvin-Helmholtz waves

Question 4

Some of these waves are important for the

Answer 4

dynamics of synoptic scale systems

Question 5

Some of these waves are important for the dynamics of synoptic scale systems, while others are merely

Answer 5

noise

Question 6

In order to understand dynamic meteorology, we must understand

Answer 6

the waves that can occur in the atmosphere.

Question 7

what are the governing equations?

Answer 7

set of equations that controls processes in the atmosphere

ex: momentum

Question 8

what does a wave mean? (particles)

Answer 8

particles are not moving (stationary)

• long wave (look like oscillation)
• wide wave (ring)

Question 9

what is the difference between oscillations and waves?

Answer 9

oscillations

• No wavelength
• can be part of the wave

sin and cosine can be applied to both

Question 10

whenever you see sin and cosine think of

Answer 10

waves

Question 11

define amplitude

Answer 11

half of the difference in height between a crest and a trough

Question 12

define wavelength

Answer 12

(,) – the distance between crests (or troughs)

Question 13

define wavenumber

Answer 13

K= 2pi/lamda

the number of radians in a unit distance in the direction of wave propagation. (sometimes the wave number is just defined as 1/lamda, in which case it is the number of wavelengths per unit distance.)

Question 14

A higher wave number means

Answer 14

a shorter wavelength.

Question 15

units of wavenumber

Answer 15

Units are radians m^-1, or sometimes written as just m^-1

Question 16

We can also define wave numbers along each of the axes.

Answer 16

• k is the wave number in the x-direction (k = 2pi/,_x).
• l is the wave number in the y-direction (l = 2pi/,\y).
• m is the wave number in the z-direction. (m = 2pi/,\z).

Question 17

The wave number vector is given by

Answer 17

Question 18

define angular frequency

Answer 18

(w) 2 pi times the number of crests passing a point in a unit of time.

Question 19

angular frequency units

Answer 19

radians s^-1, sometimes just written as s^-1.

Question 20

define phase speed

Answer 20

(c) the speed of an individual crest or trough.

Question 21

phase speed for a wave traveling solely in the x-direction

Answer 21

c = w/k.

Question 22

phase speed for a wave traveling solely in the y-direction

Answer 22

c = w/l.

Question 23

phase speed for a wave traveling solely in the z-direction

Answer 23

c = w /m

Question 24

phase speed for wave traveling in an arbitrary direction

Answer 24

c = w /K, where K is the

total wave number given by K²= k²+ l²+ m²

Question 25

For a wave traveling in an arbitrary direction, there is a

Answer 25

phase speed along each axis, given by c_x = w/k, c_y = w/l, and c_z = w/m. Note that these are not the components of a vector!

Question 26

The phase velocity vector is actually given by

Answer 26

Question 27

The magnitude of the phase velocity (the phase speed) is given by

Answer 27

Question 28

group velocity

Answer 28

(c_g) the velocity at which the wave energy moves

Question 29

group velocity components are given by

Answer 29

Question 30

The magnitude of the group velocity (...................) is given by

Answer 30

the group speed

Question 31

define frequency

Answer 31

number of waves passing through a unit time f=1/T unit s^-1 or HZ

Question 32

define period

Answer 32

he time needed for one complete cycle of vibration to pass a given point.

Question 33

As the frequency of a wave increases, the time period of the wave

Answer 33

decreases.

Question 34

define dispersion relation

Answer 34

an equation that gives the angular frequency of the wave as a function of wave number and physical parameters, w=F(k, l, m, physical parameters)

Question 35

Each wave type has a

Answer 35

dispersion relation

Question 36

One of our main goals when studying waves is to determine

Answer 36

the dispersion relation.

Question 37

Wave dispersion 1. 2.

Answer 37

1. Dispersion wave 2. non dispersive wave

Question 38

when are the waves non dispersive

Answer 38

if the group velocity is the same as the phase speed of the individual waves making up the packet

Question 39

if waves are non-dispersive then

Answer 39

the shape of the wave packet never changes in time

Question 40

when are the waves dispersive

Answer 40

if the group velocity is different than the phase speed on the waves making up the packet

Question 41

if the waves are dispersive then

Answer 41

the shape of the wave packet will change with time

Question 42

waves are dispersive if

Answer 42

the phase velocity is not equal to the group velocity

Question 43

waves are non dispersive

Answer 43

if the phase velocity is equal to the group velocity

Question 44

expression of wave by wave number and angular frequency in x- direction with time

Answer 44

Question 45

expression of wave by wave number and phase speed in x- direction with time

Answer 45

Question 46

Eulerian formula

Answer 46

Question 47

what is the difference between even function and odd function

Answer 47

Question 48

apply the even and odd function in the eulerian formula

Answer 48

Question 49

express sin (t) and cos(t)

Answer 49

Question 50

Using Euler’s formula a wave traveling in the positive x-direction can be written as

Answer 50

Question 51

a wave traveling in the negative x-direction can be written as

Answer 51

Question 52

where the amplitude A

Answer 52

Question 53

and gives information about

Answer 53

the phase of the wave

Question 54

We will frequently use this complex notation for waves because it

Answer 54

makes differentiation more straightforward because you don’t have to remember whether or not to change the sign (as you do when differentiating sine and cosine functions).

Question 55

Spectral analysis is

Answer 55

working with wave in the frequency domain instead of the time domain

Question 56

It is rare to find a wave of a single wavelength in the atmosphere. Instead, there are

Answer 56

many waves of different wavelengths superimposed on one another.

Question 57

t is rare to find a wave of a single wavelength in the atmosphere. Instead, there are many waves of different wavelengths superimposed on one another. However, we can use the concept of spectral analysis to

Answer 57

isolate and study individual waves, recognizing that we can later sum them up if need be

Question 58

So, keep in mind that real atmospheric disturbances are

Answer 58

a collection of many individual waves of differing wavelengths.

Question 59

A fourier series is

Answer 59

a way to represent a function as the sum of simple sine waves.

Question 60

A fourier series is a way to represent a function as the sum of simple sine waves. more formally, it (what does it do?)

Answer 60

decomposes any periodic function or periodic signal into the sum of a (possibly infinte) set of simple oscillating functions, namely sine and cosine (or equivalently, complex exponentials)

Question 61

Most continuous periodic functions (period = L) can be represented by

Answer 61

an infinite sum of sine and cosine functions as

Question 62

the Fourier coefficients are given by

Answer 62

Question 63

The Fourier coefficients give

Answer 63

the amplitudes of the various sine and cosine waves needed to replicate the original function.

Question 64

The coefficient a0 is

Answer 64

just the average of the function

Question 65

The coefficients a_n are the

Answer 65

coefficients of the cosine waves (the even part of the function).

Question 66

The coefficients b_n are

Answer 66

the coefficients of the sine waves (the odd part of the function).

Question 67

Smoother functions require

Answer 67

fewer waves to recreate, and have fewer higher frequency components.

Question 68

Sharper functions require

Answer 68

more waves to recreate, and have more higher frequency components.

Question 69

Broad functions require

Answer 69

fewer waves to recreate, and have fewer higher frequency components.

Question 70

Narrow functions require

Answer 70

more waves to recreate, and have more higher frequency components.

Question 71

In general, the narrower the function, the

Answer 71

broader the spectrum, and vice versa.