Quinkels tube experiment s

It is a practical proof of interference

of Sound waves

it is used to calculate the speed and

wavelength of Sound wave in a gaseous
medium
H µ sound source n

di
n

717o

F x
fixed Detector
U tube

Initially when detector reads a

maxima nth maxim

Dn 112 lil nd

Now movable tube is pulled out n

to detect neut maxima

on 2n l htt d

1
 1
An
flu di 2n nd d

rift 2n halt N

2n
I
Dm O d Iz d 31 2 21 5h12

Interference CI DI CI DI CE DI

Intensity max min max min max min

d N N
m

maxTmaxItmTxlu1maxtAn
0idz.d 321 2d 521 3d
Idf
Emine min
d d N

maxima to maxima
9k N
minima to minim

maxima to minima
On 92
minima to maxima
Et In Guin che's Experiment the movable
tube
punt is shifted by amount of 3mm
then vibration of flame becomes
maximum to minimum if frequency
of
source is 30kHz find speed and
wave length
Solan n 3mm

maximum
f to minimum
on

2n d

D Un 12mm

If
3
V 12 X 30 10 Hz

V 36o
 Beats
when two sound waves of slightly
different frregency Af L 10h2 12h2
superimpose over one another then
the
intensity of resultant wave changes
t time at particular
periodically w r a

position
This periodic variation in intensity turn in
time at a particular position is
known as beat phenomena

Sound
wave

Sound
wave

Superimpose

of 20
 N In thisphenomenon sound of
avg frequency is heared

any frequency feng AIL

2
a
Amplitude of resultant periodically varies
with time

Periodic variation in amplitude growth decay

is loudness of sound
this phenomenon of maculation in
loudness of sound is called Beats

Interference Beats
let two coherent waves Let two waves

Y a sin wt y a sin he t

Yu are sin cut 101 Yz Ceresin Wrt

Act Of constant W 2 ITF

T w 2M
time independent
wi twa
I Ii Iz 12 JI Talos
9 variable
time independent constant time dependent
I
n
I I t Iz t 2 JE Jez
Costa wait
4
time dependent
intensity
n
t
MAX Max Max
After superimposition
PT constant

IT sound
Intensity
2ft 821T min
Mf min min

stable intensity pattern

or
After superimposition
Permanent Enleurity pattern
PT variable Intensity
4T Sound 2141 821T

unstable Intensity pattern

or

tempanany intensity
pattern
one beat
one time increment or one time
decrement in intensity is known as
one beat

Max Max Max

I i

min
r Min I min
I
l
l

one beat
one beat

Beeet frequency b

b no
of beats produced per sec

b If fief of

Beat time period Tb

Tb 1
b Hi th

b 1
Beat time period
mathematical analysis

Y a sin he t a sin 2 Mf f

Y a sin Wrt a sin 2 fat

after superposition of y Q
Yz
y y 1 Yz

y a sin 2 Mf t a sin 2itfzt

y a sin 12Mt t sin 2itfat

sine sins asin cos 0

Eg 22

Y a sin at
fight
cos att
tight

29 sin 21T t Cos 2 IT t

y fifty
Amplitude
Y fi
zttzjtysinf.at
2awsfnttfti ttg
 Amplitude y resultant wave

A t
2A cos IT
ALI
frequency of Resultant wave

f fi f
avg q

final equation of resultant wave

y A Sin
2Itfaugt

hearingofBeatse
Human ears detect can beats only
upto Cloth 12h2

for b tonne 12th it appears as

constant sound
 Beats by turning forks
µ fingers

U f fz of Elo 12h

b fi ta
f fz I
Beat

case I
If f is loaded with wax

then f decreases
f Constant
b f f
tr
b will also decrease

ing f is filed
caseI
fu constant
then fi increases

b fr fr
t
b un'M also increase
 Two forks produce
EE vibrating tunning
progressive wave given by y easin Stott
and yr 2 sin 506 Itt These tanning
forks are held near the ear of a person
The person will hear u beats with
intensity nation btw maxima and minima
equal to R find value of B Q

solid Li 45in soot t

y 2 sin 506 Itt

Wi 500 IT 2 Itf fi 250 Hz

wz 5061T 21172 fz 253 Hz

Number beats b f fr
of
b 253 250

3H2Jb

Beat time period Tb

Ly f see

as we know I 2 92
I I te g 2

I K lb Ir K y
 p the CTA JT.nu
Irvin
Jr The

H t
Tin Tun

U 1212 62
4 2 22

IB I
B d g 3

II Two plane harmonic sound wave are

empress ed by the following equations

Yi Mit A sin 0.51in 1001T t

Yz Nit A sin 0.48 Itn 96Mt

AU parameters are in Mks systems
find
How many times does an observer heaee
maximum intensity in 1 see
 what is the speed of the sound

what is the amplitude of y yr at

ftp 25 see

SII a Bent frequency fi Fu

W I 00 IT Wz 96 IT

w 2 Itf 1001T Wr 221T fin 961T

HIS n fn D
the
Tb
b
ve
wz In WEL

we 1001T Wz 88 IT

k O 51T K2 Or 481T

n
iffy
soo mis

Ynet Lit L
Y _Asim Conti loont y Asin n 96kt
 at neo ta see
n
Ly
A sin Tre A sin
ye
f looetxty 9615
4
y Asin 25 it Y Asin 624 IT

y _o y o

Ynet
E
Ed Tanning fork T.fr n 300 Hr produces
5 beats sec with another T.fr If impunity
is added on the arm of known
number beats decreases
tunning fork of
then find unknown T f
frequency of
known TF Unknown Tf
g fwy
ME 3mHz
f myJosh
I 7 29542
ug
b n Nz b hz n
when is added to n its value
impunity
will decrees n te na constant

db Tb n
X
 unknown T f
frequency of 295k
Cny

A T f n 150 Hz produces 3 beats1see

having
with another Tnf As we file the arm

of unknown beats become 7 then find

frequency of unknown

N 158 Hz know T f

he 158 13 Unknown tanning fork

nz hi I 3
N 158 Hz
a
ni constant
he 155 Hz h Gl Hz
b In hat 7

Notef on
filing of T F
frequency will 9

Nz 185 Hz hz 161 Hz
Ionfiling 1 on filing
185hL 165 Hz 16542
z c
5 1614
In both cases we will get b
7J
EI 41
tanning forks arranged in a series
are

in such a that each T fr produce

way
3 beats with its neighbouring T f

If the frequency of host is 3 times of

y 1st
first then find the frequency

11th 16th gist and ith Trf

5011
zµzJ
1b b fi ta

444 444
gSt 2nd 3mg 39th moth 41M
t t t t t
f
b ft 2b f 13dB ft Uob
Wwfu 3fi
f f

f ft lo b f 1 Uob 3f
b 3
fig f t 15 b
3f
ft 40 3
2 ft Rob 25 120
ff 6oH

41 I f yob
 f Go Hu

10 3 go Hz
fi Go 1

116 Go 1 15 3 60 145 10542

f2 Got 20 3 120 Hz

fry Got 40 3 18042

Haw
Three 200
turning forks of frequencies
203 and 207 are sounded together
find out the beat frequency
TF Tfs Tfs
1
20.0hL 203 Hz 20 7 He

u
4

TF STF 3 beats in 1 see

I bent in
f see

L see
3 see
 i

i
1stBeat 2nd beat 3rdbeat 4th beat

TF f3 7 beats in 1 Sec

E I E E E E Isec

at t I see 3 beats are created

but only one will be heard

total No of beats 3 4 7 2

12
fin
 loudness is pitch of Sound
Loudness
baes's
The
quality of sound on the
of
which sound is said to be high or
LOW
It depends on

shape is size of the source

Intensity of sound
lI4A4
Amplitude of sound

Weber FenchnerLaw

According to him the loudness of sound

of Intensity E is given by

ILxtogg.IT
For two Intensity
L S
Il Iz
t t
lid Lrt dogio Iz
log Ti

tn calculated practically
 L lo dog Di Lz to log th

AL h L to dog oh lo dog o Ii

AL to toga
FF
at Ig ft loudness I D loudness
of Asian mated
units
of loudness L

unit Phon

But it is also measured in decible Cdb

zero decible loudness
L o dB

Intensity of sound at zero decible is

called thresold of hearing ero
12
To 10 Wlne
Mateo to represent the thresold of hearing
at 0dB loudness level
m
generally the loudness of intensity I
is given by compare with Io

9L Lz L T I i Io L
Iz I lez L

L to log
E
pitch
It is the characteristics which distinguishes
a shrill or
sharp sound from a

grave sound

pitch depends on
frequency
a
low
High frequency frequency
means means
low pitch
high pitch
speed of sound cu a constant
in air medium

0
air g
medium
I
fun constantl
If
woman man
If
f more fr low
a less that a more
 E so t o
9 Ga to
f to
1

Nw
him e
rn
1
dm
few 5 5 Hz firm 2h2

N woman's pitch is higher than

Mars's pitch

m
shrill pitch grave pitch
woman voice man voice
voice offrog
aka ft za
Iif D Midir