555 final crib sheet

7/25/2019 555 Final Crib Sheet

1/11

Short Answer Problem

Short Answer (Final)

Acoustic loading of a loudspeaker usually causes the natural frequency of the loudspeaker to be ___ compared to the value

it would have in a vacuum?

Reduced (due to the additional mass)

A dipole can be used to represent a source that exhibits no ___, but which exerts a ___ on the fluid at a point?

Volume change, force

A level has the units of ___? decibel (dB)

An unbaffled loudspeaker can be modeled as a ___?

dipole

*A point monopole can be used to represent a compact source that ___?

Changes volume

*A point dipole can be used to represent a compact source that ___?

Applies a force

*A point quadrupole can be used to represent a compact source that ___?

Applies a moment

A small axial fan can be modeled as a ___?

dipole

*A surface of local reaction is one whose surface normal impedance is independent of ___?

Angle of incidence

At the interface between two ideal fluids, which component of the acoustic particle velocity is continuous across the

interface? Why?

The normal acoustic impedance is continuous, to require the fluid to remain in contact

At the interface between two ideal fluids, which component of the acoustic particle velocity is not continuous across the

interface? Why?

The tangent component is not continuous, because the viscosity is small

*At the interface between two stationary fluids, what two boundary conditions apply?

The acoustic pressure and the normal components of the particle velocities are continuous

*Consider a layer of material separating two regions of the same fluid. What should the thickness of the layer be to ensure

perfect transmission?

Make the thickness of the dome to be half of the wavelength of the speed of sound in the medium of the dome.

*Consider a piston in a rigid baffle. When the piston radius is very small compared to a wavelength, the piston source maybe modeled as a ___?

Monopole against a hard surface

Consider a piston in a rigid baffle. The radiation impedance of the piston may be used in combination with the velocity of

the piston to calculate ___?

Force of the diaphragm on the fluid

Consider a piston of area S and oscillatory velocity U in a rigid baffle. When the piston radius is very small compared to a

wavelength, the piston source may be modeled as a ___ in free space having a source strength ___?

Monopole, Q = 2*S*U (2 comes from the monopole being against a wall)

Consider a square piston having a side length L and oscillatory velocity U in a rigid baffle. When l is very small compared

to a wavelength, the piston source may be modeled as a ___ having source strength ___?

Monopole, Q =2*L^2*U (2 comes from the monopole being against a wall)

Does a point monopole possess a velocity near-field? Yes (~1)

Does the sound speed depend on ambient atmospheric pressure (given that the temperature is constant)?

No, the speed of sound is nearly independent of pressure

For a uniform piston that is large compared to a wavelength, and which is mounted in an infinite baffle, sketch the

complete characteristics of the on-axis sound pressure magnitude as a function of distance from the center of the piston?


2/11

How does a pulse propagating along a tensioned string reflect from a rigid termination?

Upside down and backwards

How does the sound pressure magnitude vary with radius in the far-field of a cylindrical source?

~ *How do you find the angle at which the sound radiation from a piston in a rigid baffle is zero?

Set the angular dependent term of the sound pressure to 0 (1() = 0 ) In a public address system, why is it normal to use many high frequency drivers, and a relatively small number of low

frequency drivers?

High-frequency drivers are highly directional and ensure uniform convergence when pointed in various directions

(low frequency drivers are omnidirectional)

In the development of the wave equation for an ideal fluid, the fluid is assumed to have no ___ and to undergo ___

compression?

Viscosity, adiabatic (Acoustic processes are nearly isentropic( adiabatic and reversible for the compression process

Pressure continuity at the interface of two fluids is required to prevent ___?

Fluid separation (vacuum)

*Sound pressure is a ___ quantity, since it acts equally in all directions?

omnidirectional

The ratio of pressure to particle velocity for a freely propagating wave is said to be the ___?

Characteristic impedance

*What are the properties of a mass-like impedance?

Imaginary, positive, and linearly proportional to w

*What is a compact source?

Any source whose characteristic dimension is much less than a wavelength

What is the magnitude of the reflection coefficient at angles, greater than the critical angle?

R = 1 (T = 2, R = -1 at grazing)

*What is the mass law?

The power transmission coefficient is inversely proportional to density and frequency

*What is transverse wave motion?

Transverse waves are always characterized by particle motion being perpendicular to wave motion.

A longitudinal wave is a wave in which particles of the medium move in a direction parallel to the direction that

the wave moves.

What physical features can make a reflecting surface locally reacting?

Channels drilled into the surface.

*What two boundary conditions apply at the junction of two tensioned strings having different masses per unit length butthe same tension?

The strings must remain in contact (displacement condition)

F = ma (force condition)

When a plane wave in air hits the surface of a very deep layer of water at normal incidence, the transmitted pressure

magnitude is ___ that that of the incident wave while the transmitted intensity is ___ that that of the incident wave?

Twice, much smaller (for a very deep layer of water, there are no reflections from the bottom)

*When a plane wave in medium #1 hits the surface of medium #2 at an angle greater than the critical angle, what is the

sound field like in the second medium?

There is exponential decay of the sound field in the direction away from the interface

*When a plane wave in water reflects from a plane air surface, the reflected pressure is ___ w.r.t. the incident wave at the

surface?

Out of phase

When a point monopole is placed at the junction of three rigid surfaces, ___ image sources are required to satisfy the hard

wall boundary conditions?

7 (1 for a single rigid surface, and three for two rigid surfaces)

*When a point monopole is placed at the junction of two rigid, perpendicular walls, the sound power increases by a factor

of ___ compared to the sound power radiated by the same monopole in free space?

4 (for three rigid walls, the sound power increases by a factor of 8)

When a SDOF system is driven at frequencies well below its natural frequency, its response is controlled by ___?

stiffness

When a SDOF system is driven by an external force at its natural frequency, the system is said to be __?

Resonating OR resistance controlled

When can a reflecting surface be modeled as being locally reacting?


3/11

is independent of the incident angle *When considering sound transmission from one fluid into another, what two coefficients always sum to one?

Intensity transmission and reflection coefficients

When considering sound transmission through a limp barrier, doubling either the ___ or the ___ causes the transmission

loss of the barrier to increase by 6 dB?

Mass, frequency

*When sound radiating from a point monopole reflects from a rigid surface, the sound pressure at the receiver location is a

minimum when the path length difference between the ___ and the reflected path is ___?

Direct, half a wavelength (maximum at 0) *When the condensation at a point in a sound field is positive, the divergence of the particle velocity at that same point is

___?

negative

What is sound?

Small amplitude pressure fluctuations in an elastic medium

What is the acoustical inverse square law?

~1 Why was the reference intensity chosen to be 1 E -12 W/m^2?

It makes the sound pressure level and intensity level in a free field the same.

Short Answer (Midterm)

According to the principle of superposition, the response of a SDOF system when driven at two frequencies simultaneously

is ___?

The sum of the response to the two frequencies applied one at a time

An allowed solution of a SDOF system, is one that satisfies the governing equations, but which includes ___ that must be

determined by application of ___?

Two constants, initial conditions

An impedance of the dorm +jw17, is referred to as a ___ impedance?

Mass-like

For an undamped, SDOF system, the restoring force equation relates the two quantities: ___ and ___?

Force, displacement

For free oscillations to occur, a physical system must have both ___ and ___?

Stiffness, Mass

For wave motion that satisfies the wave equation, when 2 + 2 >2, the wave number ins the z-direction is purely___?

Imaginary

How can you determine a systems natural frequency from its mechanical impedance?

Find the frequency at which Im(Zm) = 0

Imagine a tensioned string of length L stretched between two rigid supports. Then imagine the same tensioned string held

rigidly at one end, but terminated by a point mass at the other end. Which of these strings would have the lower first

natural frequency- and why?

When constrained by a point mass, the wavelength of the first mode is longer, or has a lower natural frequency

In a SDOF system, the damped natural frequency is ___ that the undamped natural frequency.

Less than

In the calculation of sound pressure levels, why was the reference root mean square sound pressure chosen to be 2 E-5 Pa?

Lowest sound pressure audible to a healthy young adult; as a result, the sound pressure level for all audible sounds

are positive.

In the expression exp(jkx), k is the rate of increase of ___ with ___?

Phase, position

In the expression exp(jwt), w is the rate of increase of ___ with ___?

Phase, time

The equation for a SDOF system is an expression of Newtons second law:

F = ma

The motion of the mass in a SDOF system is governed by a second order, ordinary differential equation. As a results, the

solution features ___ that must be determined by application of initial conditions.


4/11

Two arbitrary constants

The natural frequencies of a tensioned string are found by solving the ___ equation?

Characteristic

The real part of a complex solution corresponds to ___?

The physical solution

The response of a SDOF system when driven at two frequencies is the sum of the response to the individual frequencies

acting by themselves. This is an example of the principle of ___?

Superposition

The restoring force acting on a segment of a tensioned string is not proportional to the slop of the segment: instead, it is

proportional to __? Curvature

The time phasor exp(-jwt) can be represented in the complex plane by a vector that rotates in the ___ direction?

Clockwise

The wave number can be referred to as ___?

The spatial frequency

The wave number plays the same role w.r.t. space that the ___ does with respect to ___?

radian frequency, time

What are the characteristics of a stiffness-like mechanical impedance?

Negative, imaginary, and inversely proportional to frequency

What is the restoring force equation for a linear, SDOP system?

= What mistake did Newton make when he calculated the speed of sound in air? Newton thought the compressions were isothermal instead adiabatic giving about 280 instead of 340 m/s

What physical property of a SDOF system controls its forced response at frequencies well below the resonant frequency?

Stiffness

When deriving the wave equation for a sound propagation in air, it is usually assumed that the compression process is ___?

Adiabatic

When driven at its natural frequency, the input mechanical impedance of a SDOF system is equal to

When the condensation is negative at a point in a sound field, the pressure at that point is ___ than the ambient pressure?

less

When the end of a string is unconstrained in the transverse direction by either a stiffness or a mass, the boundary condition

at that point is ___? Zero slope

Why are the nonlinear terms neglected in the development of the wave equation?

The nonlinear terms go to 0 (dx^2 is very small)

Why is a spherically-symmetric wave expanding into free space referred to as a 1D wave?

The sound pressure depends only on radius

Why is the convective acceleration normally neglected when deriving the wave equation in air?

It is a term nonlinear in small quantities and can be neglected compared to the first-order terms


5/11

String Problem

Governing Equation

o =1

3 General Solution

o (, ) = ( + ) o Calculate

Cancellation

o sin() =2o cos() =+2

General Formulas

o = 2 =22o = =2

General B.C.s

o () =

o Force at the middle of a string: + = 0

o Force at a simple oscillator: + = =2

o Connection of two segments: 1 =2 Mechanical Impedance

o = =o Resonance occurs when {} = 0

Power

o

=

Sketch


6/11

Pressure Problem

Material Properties

o Air @ 20: = 343 = 1.21 3 = 415

Governing Equations

o =13o =

General Solution

o (, ) =(++) General Formulas

o = o 2 =2 + 2 + 2o =, o =, o =o

= cos

1

o = cos1 o =2o =

Velocity

o =1o = + +

Cancellation

o sin() =2o cos(

) =

+

2o Replace p in the velocity equations if possible Time-Averaged Acoustic Intensity (sound power per unit area)o =12{}( ,)o ||2 = =

Specific Acoustic Impedance

o = Plane Wave Formulas

o = ||2 =2 o = 2010 2010o

=

||

2o = 1010 110o || = ||o || = ||2


7/11

Reflection/Transmission Problem (Type 1)

Problem Sketch

Material Properties

o Air @ 20: = 343 = 1.21 3 = 415

o Water (fresh) @ 20: = 1481

= 998

3 = 1.486

Governing Equations

o =1

3o =

General Solution

o (, ) = General Formulas

o = o =2o

=

Sound Field After the Interface

o (, ) = ( + ) Velocity

o =1o =1 ( +) o = (discard = )

Rigid B.C.

o |=0 = 0o T=R

o

=

o =2+2

Cancellation

o sin() =2o cos() =+2o =2 sin()o (, ) = 2cos()


8/11

Reflection/Transmission Problem (Type 2)

Problem Sketch

Material Properties

o Air @ 20: = 343 = 1.21 3 = 415

o Water (fresh) @ 20

:

= 1481 = 998 3 = 1.486

Governing Equations

o =1

3o =

General Solution

o 1(, ) =() + ()o 2(, ) =(33)

General Formulas

o = o =2o =

Angles

o =o = sin1 3 (Snells Law)

Reflection and Transmission Coefficients

o cos() =1 2 2()o

1 =

1

1

o

2=

22o = ()+()o = + 1

Pressure Amplitudes

o =o =

Critical Angle

o = sin1


9/11

Room Acoustic Problem

Short Answer

When the energy acoustics approach to room acoustics is adopted, it must be assumed that the sound field is ___?

o diffuse

At steady-state conditions, the rate at which energy is input to a space by an acoustic source is equal to ___?

o The rate of the energy absorption at the walls ( = 0, =4 )

In a normal room, the energy acoustics approach cannot be used to calculate the details of the sound decay in the first 50

ms after a sound source is turned off, because ___?o The sound field is not diffuse, or there are not enough reflections (1s in large rooms).

The reverberation time is usually frequency-dependent, because ___?

o The absorptivity of a surface is frequency dependent.

A layer of porous material is usually a more effective absorber at ___ frequencies that at ___ frequencies.

o Higher, lower

A diffuse sound field is one in which ___?

o The energy density is the same throughout the space.

When using porous material to absorb low frequency sounds, the layer depth should be ___?

o At least10to be effective

Calculation

Material Properties

o Air @ 20: = 343 = 1.21 3 = 415

Surface Area / Volume of a Rectangular Room (L x W x H)

o S = 2WH+2LH+2LW (walls + walls + floor and ceiling)

o V = LWH

Average Sabine Absorption Coefficient

o

=1

o = Reverberation Timeo = 0.161 (not including air effects)o =0 .161+4 (including air effects)o = 5.5 104 50 10001.7

Sound Pressure Given Sound Power

o Direct: 2 =4o Reverberant: 2 =4o 2 = +

Sound Pressure Level

o = 1010 (2010) Critical Distanceo =14

Time Constant

o =4 Pressure(time)

o 2() = 0,2


10/11

Dipole Problem Problem Sketch

Sound Pressure

o () = + o 1 =2o =2 o

1=

=

2 o 2 = + = +2 o () =() ()+o () =() ()+ o () = + o () =(+)() o

(

) =

+

o o () = o sin() =2o () =22 +

Zero Pressure Locations

o 2 + = 0o

2+

2=

(for

= 0,1, 2, )

o 2 +2 = 0 (smallest angle)o = cos1 o =


11/11

Piston Problem

Material Properties

o Air @ 20: = 343 = 1.21 3 = 415

Reduction to Monopole on a Hard Surface

o =2 o 1o =o

1o = 2

Governing Equations

o || = || = ||2o () =2 (pressure is twice that of a monopole in free space)

Sound Pressure Level

o = 1010 (2010)o 2 = (20106)210 Solve for ||o 2 =2 =12 2 2 =||22 2o ||2 = 2 (2)

()o || =2 (2)

() Solve for ||

o || = ||() =

o || = || (Such a large displacement is necessary because small sources are poor radiators, the location of the soundreceiver is in the far field, and according to the Inverse square law, the intensity of the source decays quite quickly in

the far field.)

Solve for o =()2o = ||2

555 final crib sheet

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