physics ia final

8/18/2019 Physics IA Final

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INTERNATIONAL BACCALAUREATEII. GIMNAZIJA MARIBOR

INTERNAL ASSESSMENT

Subject: Physics

Title: C !!el"ti # bet$ee# s%ee& ' s u#& "#& te(%e!"tu!e

CAN)I)ATE NAME: Be#j"(i# *#e+

SC,OOL CO)E: --- /0

CAN)I)ATE PERSONAL CO)E: --12MENTOR3SUPER4ISOR: G !"+& 5ibe!#"

E6AMINATION SESSION: MA7 8-1/


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I#t! &ucti # "#& the !etic"l b"c9 ! u#&

S u#& is s (ethi# th"t is "l$"ys %!ese#t i# u! li;es< but $e #e;e! st % "#& thi#9 "b ut$he!e it c (es '! ( "#& h $ l # h"s it "l!e"&y bee# t!";elli# . As " (usici"#< I "l$"ys$ !!y "b ut the s u#& th"t c (es '! ( (y uit"! "(%li'ie!< the s u#& th"t (y &!u( he"&se(it "#& the s u#& th"t (y cl"!i#et %! &uces. O#e thi# I #e;e! usu"lly thi#9 "b ut is h $these s u#&s t!";el "#& "!e "''ecte& by te(%e!"tu!e< such "s %l"yi# i# su((e! ! $i#te!.=h"t (i ht the &el"y be< be' !e the s u#& !e"ches the "u&ie#ce> ?uesti #s li9e these st"!te&i#t!i ui# (e "#& e#c u!" e& (e t st"!t 'i#&i# "#s$e!s.

The!e' !e< $he# I h"& t ch se the e@%e!i(e#t ' ! (y i#te!#"l "ssess(e#t< I 9#e$ I $"si# t e@%l !e the ;e!y i(% !t"#t !el"ti #shi% bet$ee# %hysics "#& (usic. A'te! &iscussi#

$ith (y %! 'ess !< I &eci&e& t &esi # "# e@%e!i(e#t $he!e I $ ul& (e"su!e the ;el city ' s u#& &e%e#&i# # te(%e!"tu!e usi# "# scill sc %e "#& " '!e ue#cy e#e!"t !.

The %u!% se ' this i#;esti "ti # is t 'i#& the !el"ti #shi% bet$ee# te(%e!"tu!e "#& the s%ee&' s u#& usi# !es #"#ce.

The ;el city ' s u#& is c"lcul"te& by the ' !(ul":

v = f × λ

=he!e v e u"ls ;el city ' s u#& i# (ete!s %e! sec #& m

s < f the '!e ue#cy '

s u#& i# he!t+ Hz "#& λ the $";ele# th i# (ete!s m . DThe S%ee& ' S u#& <

#.&. F1

S%ee& ' s u#& i# " ce!t"i# ("te!i"l &e%e#&s # t$ ("i# c #ce%ts: the &e#sity ' the("te!i"l "#& its !i i&ity el"sticity .

The e''ect ' !i i&ity is bse!;e& i# &i''e!e#t st"tes This is "ls bse!;e& i# s li&s< $hich h";ethe "bility t t!"#s(it the s u#& the '"stest. The# the!e "!e li ui&s "#& "t the e#& "ses< th"tt!"#s(it s u#& the sl $est.

A# the! i(% !t"#t '"ct ! th"t i#'lue#ces the s%ee& ' s u#& is the "i! hu(i&ity. As hu(i&ity

i#c!e"ses< the #u(be! ' $"te! ( lecules i# the "i! i#c!e"ses. The $"te! ( lecules h";e "

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s("lle! ( lecul"! ("ss th"# @y e#< c"!b # &i @i&e ! #it! e#. =he# the!e "!e ( !e $"te! ( lecules the!e is " l $e! ("ss t ; lu(e !"ti . This le"&s t "# ;e!"ll s("lle! &e#sity ' the"i!. The &e#se! the "i!< the sl $e! the s u#& %! %" "tes th! u h it.

The e''ect ' hu(i&ity is " little !e"te! "t l $e! "i! %!essu!es. At hi h "ltitu&es /--- ( < thes%ee& $"s c"lcul"te& t be "! u#& -.H %e!ce#t l"! e! i# 1-- hu(i& "i! th"# i# - hu(i& "i!<9ee%i# the ! ( te(%e!"tu!e c #st"#t. =he# i#c!e"si# the te(%e!"tu!e< the e''ect ' hu(i&ity $"s ' u#& t be ( &estly bi e!. B!e##"#< J.< #.&. F8

It $"s "ls e@%e!i(e#t"lly &ete!(i#e& th"t the s%ee& ' s u#& is %! % !ti #"l t the s u"!e! t ' "bs lute te(%e!"tu!e "#& the !"ti ' s%eci'ic he"ts. NASA< 8-1 F0

E@%l !"ti #Rese"!ch uesti #:How does the speed of sound in air depend on increasing airtemperature?

)e%e#&e#t ;"!i"ble:

• =";e '!e ue#cy

I#&e%e#&e#t ;"!i"ble:

• Ai! te(%e!"tu!e

C #t! lle& ;"!i"bles:

• =";e le# th $"s "l$"ys c #st"#t ' ! "ll (e"su!e(e#ts< e u"l t t$ hei hts ' the

j"! i# $hich the e@%e!i(e#t is c"!!ie& ut• The!( (ete! $"s e u"lly c"lib!"te& ' ! "ll (e"su!e(e#ts• Oscill sc %e (e"su!i# !"# e $"s 9e%t c #st"#t th! u h "ll the (e"su!e(e#ts• !e ue#cy e#e!"t ! ut%ut ut%ut $"s "l$"ys si#us i&"l $";e• Recei;e! "#& s%e"9e! ty%e b th $e!e the s"(e si(%le s u#& e#e!"t !s th"t c ul& "ct

b th "s " !ecei;e! ! " s%e"9e!

E@%e!i(e#tHypothesis : The s%ee& ' s u#& $ill i#c!e"se "s the te(%e!"tu!e i#c!e"ses bec"use the&e#sity ' "i! &ec!e"ses $ith hi he! te(%e!"tu!es< &ue t "s l"$s.

E ui%(e#t use& i# the e@%e!i(e#t:

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• !e ue#cy e#e!"t ! • Oscill sc %e• S%e"9e! • Recei;e! • The!( (ete! • J"! • P t $ith $"te! • St ;e

E@%e!i(e#t &esi # "#& %! ce&u!eI &esi #e& (y e@%e!i(e#t ' ll $i# this sche("

i!st< I t 9 " j"! ' " 9# $# hei ht 1/.K c( "#& t$ s u#& e(itte!s '! ( s u#& % stc"!&s. Ilue& #e "t the t %< $hich I use& "s " s u#& !ecei;e!< ! " (ic! %h #e. The the! #e< I lue&

"t the b tt ( "#& use& it "s " s%e"9e!. I "ls #ee&e& " the!( (ete! i# !&e! t (e"su!e thete(%e!"tu!e i#si&e the j"!.

Ne@t I c ##ecte& the s%e"9e! t the '!e ue#cy e#e!"t ! "#& the !ecei;e! t the scill sc %e t be "ble t "#"lyse the l # itu&i#"l $";e th"t ccu!s. By i#c!e(e#t"lly i#c!e"si# the'!e ue#cy '! ( s("ll ;"lues< I $"s se"!chi# ' ! the ("@i(u( "(%litu&e see# # the

scill sc %e. This % i#t is 9# $# "s the !es #"#ce % i#t< "s this is $he!e the 'i!st st"#&i#$";e ccu!s< 9# $# "s the 'u#&"(e#t"l 1st h"!( #ic th"t h"s the $";ele# th e u"l t 8le# ths ' the j"!. I' $e the# 'u!the! i#c!e"se the '!e ue#cy< $e e;e#tu"lly !e"ch 8#& h"!( #ic<0!& h"!( #ic "#& s #.

3

Receiver

OscilloscoFrequency

enerator

Jar

Thermometer

Speaker


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Picture 1: Standing waves 1

I# !&e! t i#c!e"se the te(%e!"tu!e< I %ut the j"! i# " % t 'ull ' $"te! # the st ;e. The# Isl $ly st"!te& he"ti# the % t "#& the j"! # l $ 'i!e. The he"t '! ( the $"te! $"s t!"#s'e!!e&'! ( the $"te! t the "i! i#si&e ' the j"!. I st"!te& !ec !&i# the te(%e!"tu!es sh $# # (ythe!( (ete!< "#& ' ! e;e!y ch"# e ' e@"ctly 8 *el;i#s< I ch"# e& the '!e ue#cy i# !&e! t' !( " st"#&i# $";e !es #"#ce i# the j"! "#& the# !ec !&e& th"t '!e ue#cy. I !e%e"te& thee@%e!i(e#t 0 ti(es< "#& c"lcul"te& the ";e!" e ;"lue ' the '!e ue#cy ' ! e"ch te(%e!"tu!e.

R"$ &"t" Table 1: Raw data of frequenciesT ( !"

#$%$&

f (H'"

#$%$$&88.- 1-8/ 28.- 1-/- /8.- 1- /82.- 1-8K 22.- 1-/8 /2.- 1- K8/.- 1-08 2/.- 1-// //.- 11-88K.- 1-0/ 2K.- 1-H- /K.- 11-/0-.- 1-0K -.- 1-H2 H-.- 111-

08.- 1-28 8.- 1-HK H8.- 111202.- 1-2/ 2.- 1-K- H2.- 111K0/.- 1-2K /.- 1-K2 H/.- 11880K.- 1- 8 K.- 1-KK HK.- 118/2-.- 1- / /-.- 1- 8 K-.- 110-

1 I(" e c"# be ' u#& "t:htt%s:33c#@. ! 3!es u!ces3""/H'b1 '8'-"K/"2 10Ke'8"'/&" /c bK/&-3St"#&i# =";e,"!( #ics.%#

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Figure 1: Graph of frequencies with temperature

Figure 2: ineari!ed graph of frequencies with square root of absolute temperature

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A#"lysis4el cities $e!e c"lcul"te& by the ' !(ul" v = f × λ .

Abs lute u#ce!t"i#ties:

!e ue#cy: ± 8 ,+

=";e le# th: ± -.--- (

Rel"ti;e u#ce!t"i#ty ' $";ele# th: -.0

Abs lute u#ce!t"i#ty ' the sl %e is c"lcul"te& "s h"l' ' the &i''e!e#ce bet$ee# ("@i(u( "#&(i#i(u( sl %es i# the li#e"!i+e& !"%h ' '!e ue#cy $ith s u"!e ! t ' "bs lute

te(%e!"tu!e: ± 8. . Sl %e ' the best 'it li#e is /2./ Hz√ K Rel"ti;e u#ce!t"i#ty is the#

2.5

64.6× 100 = 3.9

Rel"ti;e u#ce!t"i#ty ' s%ee& ' s u#& is3.9 +0.3 = 4.2

C"lcul"te& ;el cities ' s u#& "cc !&i# t &i''e!e#t te(%e!"tu!es "!e the# c"lcul"te& "#&sh $# i# T"ble 8.

Table 2: "alculated velocities of sound

T ( !"#$%$& ( m

s)

#)%*+88.- 02 28.- 0 / /8.- 0/K82.- 02/ 22.- 0 H /2.- 0/8/.- 02H 2/.- 0 K //.- 0H-8K.- 02K 2K.- 0 /K.- 0H80-.- 02 -.- 0/1 H-.- 0H008.- 0 - 8.- 0/8 H8.- 0H202.- 0 8 2.- 0/0 H2.- 0H/0/.- 0 8 /.- 0/2 H/.- 0HH


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0K.- 0 2 K.- 0// HK.- 0HK2-.- 0 /-.- 0/H K-.- 0K-

Figure #: Graph of speed of sound with square root of absolute temperature

Figure $: Graph of velocities of sound with temperature

As $e c"# see< the ;el city ' s u#& i#c!e"ses $ith "# i#c!e"se i# te(%e!"tu!e. By c"lcul"ti#the sl %e ' the !"%h "t the be i##i# ' ! the 'i!st ' u! (e"su!e(e#ts< $e c"# see it (e"su!es

!


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u#e;e# !"%h. It $ ul& be bette! t use s("lle! te(%e!"tu!e i#c!e(e#ts< c (bi#e& $ith " %!ecise "#& !eli"ble the!( (ete! "#& "ls " ( !e ( &e!# scill sc %e th"t c ul& "ls hel% (e"#"lyse the % i#ts # the !"%h.

It $ ul& "ls be i#te!esti# t (e"su!e the s%ee& ' s u#& &e%e#&i# # te(%e!"tu!e i# the! ty%es ' (e&iu(s "#& see $h"t 9i#& ' !"%h $ ul& ccu! i# the(. This c ul& i# the e#& hel%us t "ls "#"lyse "#& &e;el % #e$ tech#i ues ' ! !ec !&i# s u#&s th"t i#st!u(e#ts e(it< "#&&e;el % " ( !e "&;"#ce& "#& ( &e!# "%%! "ch t !ec !&i# i# stu&i s.

Re'e!e#ces

F1 The S%ee& ' S u#&. #.&. . Ret!ie;e& M"!ch 80< 8-1/< '! (htt%:33$$$.%hysicscl"ss! (.c (3cl"ss3s u#&3Less # 83The S%ee& ' S u#&

F8 B!e##"#< J. #.&. . , $ ) es ,u(i&ity A''ect S%ee& ' S u#&> Ret!ie;e& M"!ch 80<8-1/< '! ( htt%:33scie#ce. %% si# ;ie$s.c (3hu(i&ity "''ect s%ee& s u#& 88HHH.ht(l

F0 ,"ll< N. 8-1 < M"y . S%ee& ' S u#&. Ret!ie;e& M"!ch 80< 8-1/< '! (

htt%s:33$$$. !c.#"s". ;3$$$39 183"i!%l"#e3s u#&.ht(lF2 Gi"#c li< ). 8-- . Physics. ,"!l $: Pe"!s # E&uc"ti # Li(ite&.

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