hw5q kat and lina version

8/17/2019 Hw5Q Kat and Lina Version

1/9

MSE/ChBE/Chem 6751Spring 2016

Homework #5

Instructions

Bec!use this is the "!st homework p"e!se work with $our te!m to %e&ise ! sing"e te!m !nurge $ou to see me (or he"p i( $ou nee% it) one o( these pro*"ems is trick$' I wi"" &iew the retwo st!ges

1' B$ +ues%!$ ,pri" 26 e!ch te!m shou"% show me wh!t $ou h!&e got' It must *e c"e!r wwh!t-

2' B$ +hurs%!$ ,pri" 2. the re&ise% te!m homework is %ue' ,g!in it must *e c"e!r who


2/9

Problem: Speaker driver sizes

r!%ing u*ric! to c 2 points e!ch% points

+

-

As a rule of thumb, a loudspeaker driver (cone type) intended for stereo (two-channel) reproduction should not exceed in physical is required to producea !hy not" b #ow big can a tweeter be, if it must produce $%z (the upper limit of a middle-aged professor who always took good care o

upper limit of a -year-old who is into very loud music)c #ow big can a woofer be, if it crosses over to the tweeter at $%** #z" (+n the diagram below, the woofers natural inductance

crossover sometimes people run an inductor in series with the woofer)

d At what particle size must an experimenter .cross over/ from scattering of visible light to small-angle 0-ray or small-angle ne

+wow!$ spe!ker'

!' I( the spe!ker %ri&er is *igger th!n the w!&e"ength it is suppose% to repro%ucepro*!*i"it$ o( %estructi&e inter(erence incre!ses' +his h!ppens *ec!use in this spe!kers the soun% is emitte% in ! r!%i!" %irection which !s e3p"!ine% incre!spro*!*i"it$ o( w!&es c!nce""!tion %ue to %estructi&e inter(erence' +here(ore thmust *e !t "e!st e4u!" in sie !s the w!&e"ength it is repro%ucing'

*' ,ssuming ! soun% spee% e4u!" to '2 m/s


3/9

Problem: Speaker driver sizes

r!%ing u*ric! to c 2 points e!ch% points

c #ow big can a woofer be, if it crosses over to the tweeter at $%** #z" (+n the diagram below, the woofers natural inductancecrossover sometimes people run an inductor in series with the woofer)

d At what particle size must an experimenter .cross over/ from scattering of visible light to small-angle 0-ray or small-angle ne

c' ,ssuming ! soun% spee% e4u!" to '2 m/s

%' ,ssuming ! soun% spee% e4u!" to '2 m/s !n% the (o""owing "imits *etweenr!$s !n% !mm! r!$s

894: ; 1 < 42

2

/=or re"i!*"e me!surement the m!3imum 894: is > 0'? which me!ns 422/ @ 0'1 !n%

8!rtic"e sie ; >20 nm

=or &isi*"e "ight m!3 is !ppro3im!te 00 nm


4/9

8ro*"em P9θ : (or ! he3!gon

r!%ing u*ricE3p"!n!tion o( !ppro!ch 2 pointsCorrect p"ot o( 894: with no p"otting issues. points

400

A

565

A

800

A565

A

400

A

tet!;5pi/1.05pi/1.01.0pi/1.0D)n;1'5)"!m*%!;515)4;99pinsin9tet!/2::/"!m*%!:)r;00000565565.0000000565565.0000000565565.0000000565565.0000000565565.0000000565565.00D)(or i;1"ength9tet!: (or ;1"ength9r: 4r9i:;49i:r9:) 8i9i:;9sin94r9i:::/94r9i::)

en% 89i:;91/6:sum98i9i::)en%p"ot948FrF: 3"!*e"9F49,GG1:F: $"!*e"9F894:F:

11 0 ,12 00 ,

1 565 ,1 .00 ,

15 565 ,16 00 ,

21 0 ,22 00 ,

2 565 ,2 .00 ,

25 565 ,26 00 ,

1 0 ,2 00 ,

565 , .00 ,

5 565 ,6 00 ,

1 2

5 6

∑=

q P

1

$)(


5/9

Problem: Number density virial coefficient, A2

r!%ing u*ric! !n% * points

e!chc 2 points e!ch

The physics/theory community tends to prefer number density , rather than the concentration as grams/ml, w

concentration units c, we write the osmotic pressure relationship as: = cRT ( M -1 + !c + ...". #sing a symbo

coefficient when the concentration units are we ha$e

= kT (1 + A!, + ...".

%btain the relationship between A!

and A!,

.

What are the units of each &uantity'

Which pro$ides the clearer insight'

2learer insight should be better with the equation that has the number density because it is more clear tovolume with the osmotic pressure, in other words, as long as volume changes the osmotic pressure chan


6/9

o*"em +ermin!" &e"ocit$ 9!(ter !n Ho"%e 8h$sic!" Biochemistr

r!%ing u*ric!: Correct !n% %et!i"e% so"ution o(

e4u!tion*: Correct !nswer in secon%s'

3uppose at time t 4 * a force F (eg, electrophoretic, magnetic or gravitational) is applied to a spherical particle of mass m, which is initially at resmotion, balancing friction and acceleration is6 F 4 fv 7 m(dv8dt ), where f is the friction coefficient

a) +f the particle behaves as a solid sphere with radius $**9 and density of $ g⋅m:-$, solve this equation in to obtain v(t ) in terms of the partic

4 F/f

b) +f the solvent is water at *;2, find the time required for the particle to achieve


7/9

8ro*"em JS spectr!" *ro!%ening5he translational diffusion coefficient of rodlike polymers is given by

where L is the length, d is the diameter, k >T is the thermal energy and η o is the solvent viscositya) 2ompute the spectral linewidth in seconds-$ of light scattered from a rod with L4?***9 and d 4$19 in dimethylforma

viscosity *


8/9

8ro*"em Compute ="or$Huggins 8h!se i!gSt!rting (rom the ="or$Huggins e3pressions (or ! *in!r$ mi3ture 9e'g' so"&ent p"us po"$mer: computph!se %i!gr!m 9i'e' the *ino%!" "ocus: (or ! r!n%om Kight po"$mer with s ; 70' Compute the %i!gr!r!nging (rom the critic!" point to ; 1' ="or$ %i% this t$pe o( pro*"em with ! s"i%e ru"e) $ou m!$ Ln% iuse ! computer progr!m 9choose !n$ "!ngu!ge:' 8"ent$ o( str!teg$ goes into this%onNt *e sh$ !*ohints' St!rt e!r"$- Eno$- Oou c!n Ln% ! progr!m 9se&er!" !ctu!""$: on the we*site th!t %oes the c

the ke$ is knowing how it works- Pnce $ou h!&e the str!teg$ tr$ writing $our own progr!m 9or so"&e4u!tions in M!thC!% or E3ce" *ut *e c!re(u"st!n%!r% issue M!thC!% pro&es no e4u!" (or ="or$Ns s

r!%ing u*ric!: Jogic!" %e&e"opment o( str!teg$

points*: E3ecution using c!nne% progr!m

+he i%e! *ehin% the so"ution o( thispro*"em consist on Ln%ing 2 &!"ues 9!!n% *: o( the po"$mer &o"ume (r!ctionth!t h!&e the s!me chemic!" potenti!"'

+o %o so ! must *e e4u!" to *

E4' 1


9/9

8ro*"em Compute ="or$Huggins 8h!se i!g

So"&ing E4' 1 iter!ti&e"$ *$ L3ing !!n% Ln%ing the correspon%

th!t s!tisLes the e4u!tion c!n *eso"&e the pro*"em'

+he co%e use% is shown *e""ow' Hothe (so"&e9: (unction %i% not so"&e pro*"em !proppri!te""$'

hw5q kat and lina version

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