CH3: 1-D Wave Motion

Question 1

Define wave motion.

Answer 1

The motion of disturbances relative to a fluid.

Elements of Gas Dynamics, L&A, Pg. 62

Question 2

Define “Plane waves.”

Answer 2

A one-dimensional wave traveling through a tube of constant area.

Elements of Gas Dynamics, L&A, Pg. 62

Question 3

True or False
The static densities, pressures, and temperatures on either side of a shock are not affected by a transformation from the wave frame to the ground frame.

Answer 3

True.

Elements of Gas Dynamics, L&A, Pg. 63

Question 4

Define a weak shock.

Answer 4

A shock across which the normalized pressure jump is very small., e.g., (p2-p1)/p1 «1.

Elements of Gas Dynamics, L&A, Pg. 64

Question 5

True or False
The speed of a very weak shock is nearly equal to the speed of sound ahead of the wave (a1).

Answer 5

True.

Elements of Gas Dynamics, L&A, Pg. 65

Question 6

Define a “very strong shock.”

Answer 6

A shock in which p2/p1&raquo_space;1.

Elements of Gas Dynamics, L&A, Pg. 65

Question 7

What are perturbations defined relative to?

Answer 7

The fluid at rest.

Elements of Gas Dynamics, L&A, Pg. 66

Question 8

What is the definition of condensation (in terms of the perturbation theory of one-dimensional isentropic waves)?

Hint: Give the actual equation.

Answer 8

s~ = (rho - rho1)/rho1

Elements of Gas Dynamics, L&A, Pg. 66

Question 9

Define a simple wave.

Answer 9

A weak wave in which the velocity propagation is in one direction.

Elements of Gas Dynamics, L&A, Pg. 69

Question 10

True or False
Any acoustic wave may be resolved into two simple waves.

Answer 10

True.

Elements of Gas Dynamics, L&A, Pg. 69

Question 11

The lines of slope dx/dt = +/- a1 are called the __________.

Answer 11

Characteristics of the wave equation.

Elements of Gas Dynamics, L&A, Pg. 69

Question 12

The value sqrt(dp/drho)_s is referred to as ___________.

Answer 12

The wave speed or the acoustic speed.

Elements of Gas Dynamics, L&A, Pg. 69

Question 13

Why is the motion of a sound wave isentropic?

Answer 13

Because entropy production depends on the square of the velocity gradient and the temperature gradient, both of which are assumed to be negligible in the small perturbation equations from which the wave speed is derived.

Elements of Gas Dynamics, L&A, Pg. 69

Question 14

The pressure density relation in a sound wave is ________.

Answer 14

Isentropic.

Elements of Gas Dynamics, L&A, Pg. 70

Question 15

As the wave progresses through the fluid, the pressure disturbance sets the fluid in motion, giving it a velocity u, which is called the __________.

Answer 15

Particle velocity.

Elements of Gas Dynamics, L&A, Pg. 71

Question 16

How does the wave speed compare to the particle velocity (in terms of magnitude)?

Answer 16

The wave speed a1 is ordinarily much higher than the particle velocity.

Elements of Gas Dynamics, L&A, Pg. 71

Question 17

The portion of a wave that increases the density as it passes is called a _________.

Answer 17

Compression.

Elements of Gas Dynamics, L&A, Pg. 71

Question 18

The portion of the wave that decreases the density as it passes is called a _____________.

Answer 18

Expansion.

Elements of Gas Dynamics, L&A, Pg. 71

Question 19

A compression ________ the fluid in the direction of wave motion.

Answer 19

Accelerates.

Elements of Gas Dynamics, L&A, Pg. 72

Question 20

An expansion _________ the fluid motion in the direction of wave motion.

Answer 20

Decelerates.

Elements of Gas Dynamics, L&A, Pg. 72

Question 21

For a rightward propagating wave, when ds/dx is negative, there is a _______.

Answer 21

Compression.

Elements of Gas Dynamics, L&A, Pg. 72 (see Fig. 3.3)

Question 22

When ds/dx is positive for a rightward propagating wave, there is _______.

Answer 22

An expansion.

Elements of Gas Dynamics, L&A, Pg. 72 (see Fig. 3.3)

Question 23

For a leftward propagating wave, when ds/dx is negative, there will be ___________.

Answer 23

An expansion.

Elements of Gas Dynamics, L&A, Pg. 72 (See Fig. 3.3)

Question 24

For a leftward propagating wave, when ds/dx is positive there will be ____________.

Answer 24

A compression.

Elements of Gas Dynamics, L&A, Pg. 72 (see Fig. 3.3)

Question 25

When is a shocktube said to be “linearized?”

Answer 25

If the pressure difference is so small that the motion may be approximately described by the acoustic equations.

Question 26

For the propagation of a finite wave, the wave speed is ______ than a1 in regions of condensation (rho > rho1) and ____ than a1 in regions of rarefaction.

Answer 26

higher/greater
lower/slower

Elements of Gas Dynamics, L&A, Pg. 76

Question 27

In the case of a propagating finite wave, in regions of higher condensation, the ________ are inclined more since the slope is inversely proportional to the _________.

Answer 27

Characteristic lines
Wave velocity

Elements of Gas Dynamics, L&A, Pg. 76

Question 28

In the consideration of propagating finite waves, in a compression region, the characteristics would eventually cross. Is this situation physically possible? Why or why not?

Answer 28

No, it is not possible.
Because at an intersection, there would be three different values of density simultaneously.

Elements of Gas Dynamics, L&A, Pg. 77

Question 29

The front of any isentropic wave propagates at what speed?

Answer 29

The speed of sound of the undisturbed fluid.

Elements of Gas Dynamics, L&A, Pg. 78

Question 30

True or False
In general, shock waves and finite amplitude waves, in general, cannot be simply superimposed.

Answer 30

True.

Elements of Gas Dynamics, L&A, Pg. 79

Question 31

True or False
In general, shock waves and finite amplitude waves, in general, cannot be simply superimposed.

Answer 31

True.

Elements of Gas Dynamics, L&A, Pg. 79

Question 32

What is the main performance parameter for a shock tube?

Answer 32

p4/p1

Elements of Gas Dynamics, L&A, Pg. 80

Question 33

On the two sides of the contract surface, the pressures and fluid velocities are _____, but the densities and temperatures are ________.

Answer 33

Same
Different

Elements of Gas Dynamics, L&A, Pg. 82