I year physics

1. UNIIT-3
Waves in
3kunas and pipes
DATE
Mechanical taves
hedislunbomCe.ehch Callp eoRa Omd
mometum om ova
point in spate ano ha
Pointi in spaCa ahowt tHatroms
D
i ka mediom
Rnown as a Oave A
Formaion 4 aveson sReteed sns
cE us +ake a Lemg slgsOrn ol t one end
the Slkuiia tke . ive a quiek jer
abump
pulse) ia produa.ad inhe sRing. Such
. .
olurbomto i udoda and tLasbfer 3h0r
cunation
onhene 8Rnoun a Aare fulse. T
esRs du iven Con-tinuowsty then ho uaves Poclutad
Osa Stomding Oa veS ca +somavAse ave
Oa Vee
as VeTSe Oave
T+is deinadQs Oave sheae he movemen
Paxicles i mediu is pependieulav o tha clRaatton
the
propagoion Oave.
The periool b oave i indlisack pProperhna)s e t e
* * * *
RA coave T: 4
3 he Spea4 Coave 1S Poopo-ional Oayelougf &
th
direct popotomal 5The Peiod Re ave.
e
V:AlT
Kelationship bet gyeny omdPeoiood, V Af
4)
rest e
ough

2. 0ATE
aves in Pipes
Ppes Prooutis3tmdnq uoavesSimilas ts
SRRbichad Stngs. Ln ie pipes a oaves ana litudinal
Longtudinal oav
Yanth cles Re cöave vibzate în Same line Gs tA
ilio 4-savel
Closad Pipes
P 4Aesèt a à ndes is at a arHnode
Nodos a aluwaysomes a clesed end g Ppe
WheiL au Cawnet move.
Artinodes a alwaysokoed at Ra open end Pipe.
Distomee belwean node and atinode
avelangh N AN
P
Y4 n-lsr harmon
NA
Funda.mendal mode Vbta-ionL
AN
AN
+ 8
N
AN
AN
n 3 harmonie
A 4
a 8 5 : : .
(an+

3. Valouly onsveaseOave inaSRetehe Shing
TNP
Imms neRse
let Compul 4A Velouy
ravelling
traxelling0aves
On a Shing, W a erK is 7ven
at one end Ha lepe h ave move a0ards
ug hdwt veloiuty Vw.r.t obgesver.
Contdae an elemente segment In theAhing
Os Shouon in g. e A &B be. lwo polnts on
he Staing at an instomt tme, lot dl and dm
be the leigth omd. mas Ra elamuntal &ung .
ineamas densul dm dl
in
poinTS
e em oll. 0
Th-elumental skmg ABhsa Cuvaliu Look ke
sc aele, w Cbu at 0, iodlls R
Omd aRc Sublendmg by an nglu Oat the lgn .
l ane lnah
R a d t us
thContupetal acealnalim Buppluès y lensum iy
skun
Canbi
pe on ce
R
8ub dm a u in
J d V 4 )
R
R
lerslonT ca t alna htengtnt tA
AB. ince
elemonFalsegment 4 sumg AB. gince
the asc length
s vemy mali Vaiialt in Tersir
OA Com begnoaed
We Can esolveT Intohonizonta) Cemponent
T Ces ) md Ve-ical Corm ponan T Sn).
heboiZentad Corppnentsat AKBa2 2qual in mnagnir
but oppesieinodiredin s0 Ry Comee) oher.
The Vestical Componen at AaBppears qu
Vetcal touardls CedRa anC omd ante thu
hance hu
TNPL

4. T cos
Ax
T cos )
V(pulse)
T
Ar T
Note
T sin G) sin G)
R
V (pulse)-
O
Figure 11.15 Elemental segment in a stretched string is zoomed and the pulse seen from an
observer frame who moves with velocity v.
UNITII WAVES

5. add upThe net Aadleal ontu F
TSin9
uoaN Veny Small we
nce +Ranmpiluide
Compased wthongth4 Shung
Sin2):
T TO
Bu d 1 d
R R
pPyin Nawtons seumd a lo a elumental
gking n the Taclial dunlimy Reradial lomporen
4or equal to e Cotipetal orta
4Hence equatng & a
Td
R R
Uv dt
Rosul
adic popational tothaSquak oot
R nsio e
b)invessael PopotHona ta Aa quase Ap
nasnass dnaua
dpen dant hapc aNts.
Neton -JovrouJa er Spud ound uaver in Cir
Sir saac Nwto0O8umad hat win 8ound
Prepoga na Re
d oabmaRes plateiu isotkermal n nalida
)The heot Produced duing ompkesaiou CPC38
nLassVOlumedeiasosand'heat is ost durtn
PaRLactHon PReku deeDasLAVol neucasesSo
oTmam Compression
emp medwm AomainsCmstamt

6. ByAauna the
3) au molecules torm an fdeal
D
a h chomgs in PAesua Onel volume bey
Boyles law
PV Constont O
D haung Pdv +VdP 0
P VdP (
Ki , is0thermas bulkmocduluS a
Sub eas, in.eqp y
he Speas Soun d in as
PAes une hese Valuu ar NTPCnormal
empesalus Omd PAamsua) is 76 ro q mar Cr
Ph9
07X 13-6 xto x 9.8N m
j 213 Rg lm
Then perd 60und in_au oat NTP i6
isRe deniday a3
x t3.6 x tox a.8
219. 80 os 28o.ms
Buwt hai 8peoa Soune n ok at 0C
expeoimen ally ebseved 332m|S,_whieh is
closeupts14 moe hounheoRAtical Value
****
.errDr 38 28o n100= S.6 Y. Thio esror
8rmatl.
Laplaces Corecho
I n 181b aolace atsacotily meced this
dieponme by oSUminghab tuhen Sound
Propagaiswnouah a medrum,fhe partcles osallol
hopagati,
VerRapid,Auoh -haut Comptashion omd Rasjaction
OCcr Very as
enc Me Rzchomgt4 htat Dto duerd duu t
Compussion OmdCoelin et du Rataction
do hot ak pla t, because ain madium isbad
Condulor a b

7. C inte jemp
C
18 no
Congo C6sictaa.d as a
Cons Fomt hote 8ounel Propaqalim s h adiabale
By adiaboH c conl leRali
ta
PV Constown+ O
whe v -Crc which Rato bet Speukt haas
Volume
a Csns PLexuth om d peeikchaat at Cmst
D ntiading ,
V'df+ P(vV dv 0
-
P(vV dv)=-V dP
P
Vdv
P-Vdp
dv
KA .
whee Ka adiabotic bulk moculus .
Now 8ub he 9peced Sound in a
KA
au Contams mamly nimgen Oxy2 drmgtu
Cciadomic gas) D HencaSp2cel
Soundl in a Va14 280m9)33130m/s
data
whic tVeR uek clete enpeumontal data.

8. Facfors aleelmg Spoo.d Sound ih 9e
Un ola.a as n
Lo
PV ALR
Presue V volume T is leap, n
mole Uoivetsa gasi Cma.
amole cult
PV= Cmt
4or ven P as
o, densil as invaasely Vades
For ata mass
oit Volume.t
C3)
Sub in
C o a t
T CsT CT
Qvenin eqn (laor
the Spead
Sectid
S0un d
V yCT
o) For a ixa d emP , kessunebecomes
Vasus, Cms
olansik
a ec ressuke
J
Comgt
also Vasus, Suchhat
Aatio e) becomes Const
Tho meoms Speed
sound is indepene osu
For a
ec
Jemperadui
emp
a m a w s S a m e
6 top bollom mounan
espeed, Sound cOil emain ame at these
lwo pbin
u tn PracHCe twonf be 8ame,hence speed
Sound solfesant act di etaut ptints
bEfect
hence Spead
Tempera lume
V VT
Spead Sound Vaxte olixect to Squake noot
lmp in Celvin
o4 Vbe peed Sound at emp at oc or
&13k
Cmd be Re speed sound
at ang asbkkaryemp
or 73k

9. hen 73 +6
V V18 13
Vot+ Vo14 binomia)
546 xpanston
7 3
SinceV 3 m/s a OC, Vat any emp in
t'e is
V-331+ 6.6te ms
Thus the pord Sound in a nccases by o.61hms
per cleqen celers vise ih tenp
henemp in aeasesihe molecules coill ibsal
as ti due to Jan thermal nergy md hente
peed sond in cReas es
feetf humid Cmoislure
Desly..mefs a is .6 9 hat d
aU, shich nmeas, he pResente moisfe A
Cin cease in hurmidly)dactenes olensily .
ThexezoreSperd 30und inaeasea with ise
nhumidil
*
V Y VyCT
a p d a Va be donsu mot 8pecd
s6un in dj a Thon
Pis totali atmosphexei PRosua Atcorelin
ts liors s taw q pasttal. PAsosua, it Cam be
Shoon
6 25 P
aaseHe artal Presua dy a
talar Vapour Kspectiveu The
P

10. dE
ec densilg:-
Coni der lw 9apes ofb duei dons ulie
havin erop
same ernp omd pressume. Then thepea4
oo V,= P
s0und in
Takmq Aato
VP
V
V
s0und in a 9as is in veas e
denilg 3
Ths 4 velo ly
Propoonal t t
Squatea root
a s .