22 pius augustine sound, echo and resonance

SOUND
Echo
Resonance
Characteristics
Dr. Pius Augustine, SH College, Kochi

SOUND
Invisible waves
moving through the
air around us.

Revision
• Sound is produced due to
vibration of material bodies
• It is a mechanical or elastic wave
• Speed of sound depends on
density and elasticity of the
medium
• Audible range is 20 Hz to 20KHz.

Revision
•Sound freq greater than 20KHz
- ultrasonic sound
•Sound freq less than 20 Hz -
infrasonic
•Speed of sound in air at 0 oC =
332 m/s and at room
temperature is 340m/sDr. Pius Augustine, SH College, Kochi

Range of hearing
Audible range – 20Hz to 20 KHz.
Varies from person to person.
Decreases as getting older due to reduction
in sensitivity of ear to high frequencies.
Children - upto 30 KHz.
Old person - below 12 KHz.
Most sensitive range - 2Kz to 3KHz.

Infrasonic : freq < 20 Hz
Utrasonic : freq > 20 kHz
Dog – hear upto 50kHz.
Bat – upto 150 kHz.
Elephants and whales – produce
infrasonics

Revision
• Aero plane with speed greater
than speed of sound (Mach -1) –
supersonic
• Speed greater than Mach 5 is
Hypersonic

Revision
• Sound is longitudinal wave travel as alternate
compressions and rarefactions
• (But in solid rod or bar, rod expands sideways
slightly when it is compressed longitudinally
(similarly on the surface of liquid)
• Velocity of a wave v = fλ, f – freq and λ –
wave length

When a wave travel from one
medium to other (frequency – no
of waves produces per second does
not change) but velocity and
wavelength changes.

λ = 0. 20 m . V = 24 m/s
i) f = ? ii) T =?
f = v/λ = 24 / 0.2 = 120
T = 1/f = 1/120 = 8.3 x 10-3 s
For the solution of the problem shown, prepare suitable
question
The wavelength of waves produced on surface of water,
given wavelength and velocity. Find frequency and time
period?Dr. Pius Augustine, SH College, Kochi

Characteristic of wave motion
• Periodic disturbance advancing through the
medium without actual transfer of particles of the
medium (energy transfer at constant speed)
• When two or more waves arrive at a point at the
same instant, total displacement of the particle is
the vector sum of displacements due to individual
waves - super position of waves.

Characteristic of wave motion
• Speed of energy transfer (wave) depends on
the nature of the medium
• When wave travel from one medium to
another medium, speed, wavelength and
intensity (reduction due to partial reflection)
and direction (except at i =0) change but the
frequency of the wave does not change

Distinction between light and sound
• Light wave
EM wave
• Can travel in vacuum
• Speed in air = 3 x
108m/s
• λ very small 10-6m
• transverse
• Sound wave
elastic or mechanical
wave
• need material medium
• Speed in air = 330 m/s
• λ vary from 0.01m to
10m
• longitudinal in air

Reflection of sound
Sound like light obeys laws of reflection
angle of incidence = angle of
reflection
incident wave, reflected wave and
the normal lie in the same plane

Reflection of sound
Smooth surface which reflects sound (XY)
keeping tube A and watch stationary, hearing
tube is moved and distinct tick of the watch is
heard at a particular position.
Angle of incidence = Angle of reflection
Angle i = angle r

Practical Applications of reflection of sound
Megaphone or speaking tube
horn shaped metal tubes from which
reflection of sound take place, which
prevents spreading of sound

Practical Applications of reflection
of sound
Ear trumpet or hearing aid
Narrow end of ear trumpet is kept in the ear
hole of the person who is hard of hearing and
wider end faces towards the speaker, which
increases the intensity of the sound due to
reflection

Practical Applications of reflection of sound
Sound boards : Sound boards are concave sound
reflectors used in auditoriums in such a way that
the speaker is fixed at the principal focus of the
sound board.
Reflected sound parallel to the principal axis reach
everyone in the audience clearly

Echo
Sound reflected from distant object such as
high building or hillock, reaches back
after the original sound ceases so that
the reflected sound appear as repetition
of original sound.

• Persistence of hearing is 1/1 0 sec (0.1sec).
• For getting echo, reflected sound should reach
after 0.1 s.
• If v is the velocity of sound and d is distance
to the obstacle, and t is the time for sound to
reach back
• V = 2d/t or d = vt/2

• V = 2d/t or d = vt/2
• Min. distance required for getting echo
(for man) d = v x 0.1 /2 = v/20 metre
• In air v = 340 m/s
• d = 340/20 =17 m.

Conditions for formation of echo
• min distance to the obstacle
d > or = 17m
• Wave length of the wave should be
less than the height of reflecting body
• Intensity of wave should be sufficient
enough

In water
minimum distance between source and
reflector to hear echo distinctly is
d = vt/2
= 1400 x 0.1 /2
= 70m

d = 48m v = 320 m/s
t = ?
t = 2d/v = 2 x 48 /320
= 0.3 s
Question please?
A man standing 48m away from a….

f = 5 T =1/f=1/5= 0.2s
t = 8T = 1.6s v = 340 m/s
d = vt/2 = 340 x 1.6 /2
= 340 x 0.8
= 272m
Question Please
A pendulum has a frequency of 5 vib.
Time required – 8 pendulum oscillations
d?

Ultra sound is preferred for echo sounding
Give reason
Ultrasound of frequencies of the order of
50,000Hz is used.
i. Can be confined to a very narrow beam and can
penetrate great depths of sea water without
much loss of energy.
ii. Will not be confused with engine noises or other
audible sounds.

New Antarctic Seabed Sonar Images Reveal Clues to Sea-Level
Rise

Sound ranging or echo sounding
Process of finding the distance of objects by
using reflection of sound.
Eg: depths of oceans and lakes, locate shoals of
fish, locate submarines.
Reflected sound will be received by a special
type of underwater microphone, called a
hydrophone.

SONAR
Sound Navigation And Ranging
Principle of echo sounding is
extensively used in this
instrument.

SONAR : sound navigation and ranging
Used to locate submarines or shoals
of fish or depth of ocean bed.
If ultrasonic sound is used - is called
ultrasonic ranging or echo depth
ranging.

• Noting the time gap (t) between sending
of original sound and reception of
reflected sound ‘d’ can be determined
•d = vt /2.
• v – velocity of the sound wave in the
water [ 1450 m/s ]

v = 1400 m/s t = 1.5s
Depth = ?
d = vt /2
= 1400 x 1.5 /2
= 1050m
Question please?
On sending ultrasonic wave…..

d = ? v = 1450 m/s t = 4s
d = vt/2
= 1450 x 4 /2
= 2900 m = 2.9 km .
Question please?
A ship on the surface of water …..

RADAR
Radio Angle detection and ranging
•Sending radio wave (em
wave) to air to locate enemy
aero planes.

d = 45000 m v= 3 x 108 m/s
t = ?
t = 2d/v
= 2 x 45000 /3 x 108
= 3 x 10-4s.
Question please?
A RADAR sends a signal to an aero…

Echo - applications
• Dolphins: have sound sensing system which
enable them to avoid fishing nets and other
objects using echo of the sound produced by it
• Echo is used to locate gun positions of the
enemy
• Echoes are used by geologists for mineral
prospecting.

How do bats avoid obstacles in their way
when in flight?
Bats can produce and detect the sound
of very high frequency up to 100kHz
(ultrasonic sound)
Bats fly with speed much lower than
the speed of sound
Echo of sound help them to identify
the obstacles in its path.

Ultrasound sensors for parking space measurement

Reverberation
It is the prolongation of sound due to
the repeated reflection of sound from
near by objects
(reflected sound reaches back before
the original sound ceases)
eg. Rolling sound in large empty room

Finding speed of sound in air - Echo method
Select a high rise building at least ½ a km
away (x) and fires a powerful cracker.
Note time t1 for echo.
v = 2x/t1.
Repeat it after moving a distance d away
(d>150m ) and note t2.
v= 2 (x + d )/t2
• Solving, v = 2d /t2-t1

t1 for travelling from P to C1 and back = 4s
t2 for travelling from P to C2 and back = 6s
If x is the distance b/w C1 and C2,
time taken to travel 2x = 10s.
2x/10 = v or x = 3200/2 = 1600m
Question please? Best suited…
A person standing between two vertical walls x meters
apart. X ? Sound is produced by the man and hears
echo…..

An observer standing between two
cliffs fires a gun. He hears the first echo
after 1s and the next after 2 more
seconds. Find i) his distance from the
nearer cliff and ii) the distance b/w the
two cliffs. V = 340 m/s

Time to hear echo (case-1) t1= 5s
Distance move towards d = 310m
Time to hear echo (case-2) t2= 3s
Speed = 2d / ( t1 – t2)
= 620/ 2
= 310 m/s
Question please
A man fires a gun and hears its echo ….

Expt. Speed of sound
A and B at high altitudes having separation
d (1km or more) in air.
Observer A fires gun and B starts clock on
seeing the flash of light.
Stop the clock on hearing sound
Time is noted as t1.
Now B fires gun and as before A noted time
t2.
V = d/t, t – average timeDr. Pius Augustine, SH College, Kochi

Direct method
• Let A and B are two high rise location
having separation move then 2km.
• A person at the location A starts a stop
clock on seeing the flash of the gun fired
at B and stopping on hearing the sound .
velocity of sound V = d / t.

Free or Natural vibrations
The vibrations produced in a
body, on being slightly
disturbed from its mean
position are called free or
natural vibrationsDr. Pius Augustine, SH College, Kochi

Vibrations with constant
amplitude and constant
frequency

Natural time period
Time period of a body
executing natural vibrations is
called natural time period.

Natural frequency
Number of vibrations executed
per sec by freely vibrating
body is called natural
frequency.

The period or natural
frequency of vibration
depends on the shape and size
(or) structure of the body

Eg : 1. Stretched string is plucked , it
executes free vibration
2. Simple pendulum pulled to
extreme position and released
3. Tuning fork on struck with
rubber pad

4. Metal blade -clamped at
one end is gently disturbed.
5. Loaded spring- load is
pulled a little down and
released

Simple Harmonic motion
Periodic motion in which, restoring
force (accn) of particle is directly
proportional to displacement from
mean position and directed towards
the mean position.

Draw a graph between
displacement from mean position
and time for a body executing free
vibrations in vacuum?

Air column in an organ pipe is
made to vibrate .
(natural frequency is inverseley
proportional to length of air
column)

For a pipe opened at both ends
(open pipe) frequency is in the
ratio 1:2: 3 ….

And for closed pipe (one end
closed) freq is in the ratio 1:3:5……

Note: If there is no resistive forces, the
total mech. energy is constant and
oscillate forever with no decrease in
amplitude.
Such a motion is called undamped
oscillatory motion (possible only in
vacuum)

• Graph showing undamped free
vibration

Damped vibrations
• Periodic vibration of continuously
decreasing amplitude are called damped
vibrations
• The decrease in the amplitude caused
by dissipative forces is called damping
• Eg previous five examples in air

• Graphical representation of damped
vibration

Damped helical wave

Forced vibration
When a body is maintained in a state
of vibration by a periodic force of
frequency other than the natural
frequency of the body, vibrations are
called forced vibration

Eg. 1. vibrations of board of a guitar, when
the string is made vibrate
2. Loud sound is heard on pressing the
handle of a vibrating tuning fork against
table top.
[Tuning fork forces the table top to vibrate with
the same frequency. Large area of table top
gives louder sound]

• Wind box of stringed instruments are
forced to vibrate by the vibration of
the string
• Tones conveyed from the record
vibrates the diaphragm of gram
phone sound box

Characteristics of forced vibrations
Forced vibrating body acquires
the frequency of driving
periodic force and not the
natural frequency of the body

• Amplitude of the forced vibrating
body is inversely proportional to the
difference between the natural
frequency of the body and the
frequency of driving periodic force .

If the frequency of the driving force
is exactly equal to or integral
multiple of freq of vibrating body
,amplitude of oscillation is very
large.

Resonance or Accoustic Resonance
• The phenomenon of setting a body
into oscillations (high amplitude)
with its natural freq by another body
vibrating with the same freq is called
resonance.

Conditions for the phenomenon of resonance
• Natural freq of the driven body must
to be equal to or integral multiple of
the freq of driving body.
• Driving body must have sufficient
force to set other body into
vibrations. Dr. Pius Augustine, SH College, Kochi

Differentiate between forced vibrations
and resonance.
Forced vibration
Driving frequency is not
equal to driven bodies
frequency
Amplitude is not max.
All forced vibrations are
not resonance..
Energy is not max.
Resonance
Add here

Eg: 1. sympathetic vibrations :
Two tuning forks A and B of same freq are
mounted on two sound boxes such that
their open end faces.
A small hanging pith ball touches the
prongs of B .

Eg: 1. sympathetic vibrations :
Strike the prong of A with a rubber
hammer. B starts vibrating indicated by
the movement of pith ball.
Sound waves of the first fork causes the
second to vibrate. This phenomenon is
called sympathetic vibration.

A
B
C
D
Sympathetic vibrations.

Consider four pendulums A, B
,C , D as in fig, with length of A
= length of C and length of D
greater than and B less than
that of A or C.

If A is given a small oscillations C
oscillate with greater amplitude and
in phase.
B and D oscillate with lesser amplitude
and out of phase with A and C. ie. C
is in resonance and B and D are in
forced vibrations. Dr. Pius Augustine, SH College, Kochi

Examples of resonance
Motorcycle vibrates violently when bike is
running at a particular speed. [Natural
freq of frames matches with that of
engine piston]
• Particular railway compartment makes lot
of noise.

If the speed of vehicle is increased
or decreased, resonance will be
disturbed and violent vibrations will
be stopped.

Why is a loud sound heard at resonance ?
Body vibrates with large amplitude
at resonance and conveying more
energy to the ears.
Hence loud sound is heard.

Soldiers are asked to break their steps
while crossing suspension bridge
[If freq of steps matches with the
natural freq of bridge, bridge may
collapse due to resonance]

• sometimes wine glass vibrates when
a particular notes is struck.
• Resonance can cause disaster during
earthquake [when freq of building
matches with that of earthquake
wave freq] Dr. Pius Augustine, SH College, Kochi

Examples of resonance .
Radio and T V reception [Tuning] Capacitance
of variable capacitor is adjusted until freq
of LC oscillation is equal to freq of the
signal transmitted by particular station.
Electrical resonance picks up particular
station signal.
• Sound box of musical instruments

• Resonance in air column:
If an excited tuning fork is held at the
mouth of a water filled burette and
length of the air column above the water
is increased by releasing the stopper, a
booming sound is heard for a particular
length of the air column

Then natural freq of a particular
length of air column matches
with freq of tuning fork

Standing wave formation in the air column.
• Vibrating tuning fork sends a
compression into the air column within
the burette which will be reflected by
the water surface (denser medium).
Reflected compression on reaching the
mouth of the burette is change into
rarefaction.

Standing wave formation in the air column.
• If the length of the air column is such
that, during this time, if the tuning
fork produces a rarefaction, two
rarefaction superimpose and a
booming sound will be heard.

Vibrations in stretched string
• Law of length :
Freq of the note produced by a stretched string
is inversely proportional to its length .
ie. f α 1/ l.
• If there are two strings of lengths l1 and l2,
such that their frequencies are f1 and f2,
then f1 / f2 = l2 /l1

Law of tension:
Freq of note produced by a stretched string is
directly proportional to the square root or tension
in the string
f α √T.
• For two strings with tension T1 and T2 , and having
frequencies f1 and f2 ,
• then , f1 / f2 = √T1 / √T2

Mass or thickness of string :
Freq of note produced by a stretched string is
inversely proportional to the square root of
mass per unit length (linear density) of the
string .
If m - is the linear density,
f α 1/√m
or f1 / f2 = √m2/√m1.Dr. Pius Augustine, SH College, Kochi

Vibrations in stretd string
• Combining the three laws
f = k T = k T
l m l ρᴨr2
for fundamental note k = ½.
• Linear density
m = mass/l = MA/lA = Mᴨr2/V =
ρᴨr2

Frequency is inversely proportional
to radius or thickness of string
and inversely proportional to
square root of density of the
material of the string .

Note 1.
• K depends on the no. of loops
formed during vibration
• For fundamental note or principal
note or first harmonic (single loop) k
= ½ (two nodes and one antinode)Dr. Pius Augustine, SH College, Kochi

Note 1.
• For two loops (first overtone or first
octave or first subsidiary or second
harmonic, k = 2/2 = 1.)
• In general for p loops, k = p/2.
• For pth overtone or (p +1)th harmonic,
fp = p/2l √T/ √m Dr. Pius Augustine, SH College, Kochi

In general for p loops,
for pth overtone or ( p +1 )th
harmonic , k = p/2.
fp = p T
2l m

Experimental study -sonometer
Consists of a hollow wooden box
A string has one of its ends attached to
fixed support S and is passing over a
smooth pulley and a weight is
attached to the free end

vibration of stretched string - sonometer
•Two wedges w1 and w2 are
placed below the wire and a
small paper rider R is placed
over the wire

vibration of stretched string - sonometer
• Press the stem of excited tuning fork
on the sonometer and adjust the
length of the string between wedges,
until the string vibrates in resonance
with the vibrating tuning fork and
paper rider flies off.

Experimental study of vibration of
stretched string - sonometer
Freq of vibrating string
fp = p T
2l m
= freq of tuning fork
(resonance)

A blade fixed at one end, is made to vibrate
by pressing its other end and then
releasing it. State one way in which the
frequency of vibration of the blade can be
lowered.
Increasing length.
Sticking small wt at free end of the
blade. Dr. Pius Augustine, SH College, Kochi

Why are the stringed instruments
provides with a sound box?

Musical sound
i. Produces pleasing effect
ii. Proceeds at regular
intervals in quick
succession ( periodic
vibrations)
iii. Waveforms are similar and
no sudden changes in
loudness , freq or
wavelength.
iv. Sound level is low (<30dB)
Noise.
i. Displeasing
effect
ii. Proceeds at
irregular
intervals ( non –
periodic)
i. Sudden changes
in loudness , freq
and wavelength
i. High ( >120 dB)

Characteristic of musical sound
i. Pitch or shrillness
ii. Loudness or intensity
iii.Quality or timbre
Note:
loudness and pitch are subjective
Intensity and freq are objective.

Music is the art of sound.
Music is sound that's organized by people
on purpose, to dance to, to tell a story, to
make other people feel a certain way, or
just to sound pretty or be entertainingDr. Pius Augustine, SH College, Kochi

The dynamic range of human hearing
and sound intensity spans from 10-12
W/m2 to 10 - 100 W/m2.
The highest sound intensity possible to
hear is 10,000,000,000,000 times as
loud as the quietest!

Intensity
Objective property and
independent of response of
the ear of the listener.
Unit – J/s/m2. or W /m2.

Intensity – objective (measurable) property
Intensity at any point in a medium
is measured as the amount of
sound energy passing per second
normally through unit area at that
point

• Sound intensity is defined as the
sound power per unit area.
• The intensity is the product of the
sound pressure and the particle
velocity

Loudness
Is a subjective property of sound by
virtue of which a loud sound can
be distinguished from a faint one
both having same pitch and
quality

• Strike a tuning fork softly – gives faint
sound,
• strike it harder – gives louder sound
of same frequency.
• If wave forms are analysed in the both
cases, frequency and wave form will be
same, but amplitudes will be different

Loudness depends on amplitude or
(intensity) of the wave.
Loudness is not the same as intensity.
Intensity is a measurable quantity -
objective, while, loudness is a
sensation, subjective

Factors affecting the intensity of sound ( loudness)
Intensity α
i. amp2
ii. 1/d2. (distance b/w source and
listener)
iii. Density of medium
iv. Area of vibrating surface
v. motion of the medium
vi. Presence of resonating body
Loudness depends on frequency in addition to
above mentioned factors. Dr. Pius Augustine, SH College, Kochi

• The sound intensity decreases with
distance to source. Intensity and
distance can be expressed as:
•I = P/ 4 π r2
• Where P = sound power (W)
• π = 3.14
• r = radius or distance from source (m)

• The connection between Sound Intensity
and Sound Pressure can be expressed as:
•I = p2 / ρ c
• where p = sound pressure (Pa)
• ρ = density of air (1.2 kg/m3 at 20oC)
• c = speed of sound (331 m/s)

Loudness
Loudness of sound is the magnitude of auditory
sensation
Subjective property
Depends on the intensity of sound and response or
sensitivity of the ear. (sensitivity of ear depends on
frequency)
Magnitude of loudness is proportional to logarithm of
intensity ie L α log10I

•If intensity is multiplied
100 times, loudness will
be doubled.

Note .
Intensity of 10-12 W/m2 at 1kHz freq is the
threshold audibility of human ear and is the
zero level of intensity (I0)
Intensity below this at frequency is not audible
Corresponding loudness
L0 =K log10I0. → 0 dB

Weber – Fechner’s relation
L = K logI
K - const of proportionality

Note .
For higher intensity I1, L1 = Klog10I1
Constant K depends on unit.
L1 – L0 = L = K log10(I1/I0)
If K =1 , corresponding unit is known as “bel”
L = K log10(I1/I0) bel.
L = K 10log10(I1/I0) dBDr. Pius Augustine, SH College, Kochi

•If I1 = 10 I0
• L = log10 10 = 1 bel = 10dB
• 1/10th of a bel is decibel. Or
• 1bel = 10decibel
• If I = 100 I0 , loudness is 2 bel.

Note!
In US a reference of 10-13
watts/m2 are commonly
used.

Unit of loudness
• Decibel -The decibel is a dimensionless
quantity.
• Phon.
Loudness of any sound in phon is equal to
loudness in decibel of equally loud sound
of frequency 1kHz.

• Increasing the sound intensity by a factor of
• 10 raises its level by 10 dB
• 100 raises its level by 20 dB
• 1,000 raises its level by 30 dB
• 10,000 raises its level by 40 dB
• and so on

when a tuning fork is struck, the
sound is omnidirectional (heard in
all directions)
Because the sound waves spread
out in all directions.
(mega phone restricts)Dr. Pius Augustine, SH College, Kochi

Pitch or shrillness
Is the sensation which determines the
shrillness of sound.
(helps to distinguish acute or shrill note
from grave or flat note)
Is a subjective property .
Independent of loudness and quality.
Depends on frequency (wavelength) and
relative motion between source and the
listener. Dr. Pius Augustine, SH College, Kochi

When two notes have same frequency,
they are said to be in unison.
Pitch α freq
Freq α 1 / λ
Pitch α 1 / λ

Quality or Timbre or Tone colour
Characteristic which distinguishes the two
sounds of the same loudness and same
pitch, but emitted by two different
instruments.
Depends on wave form (ie. Number of the
subsidiary notes present)

Sound of single frequency is
called pure note or tone.
Eg: produced by tuning fork
(sine curve)

Note:
Sound from an instrument contain a lowest
frequency ( having highest amplitude )
called principal or fundament frequency,
along with intiger multiples of
fundamental frequency (having small
amplitude) called subsidiary or
secondary vibrations. Dr. Pius Augustine, SH College, Kochi

Note:
Wave form of an instrument depends on
the presence and relative amplitudes of
the various subsidiary vibrations in
comparison with principal vibrations.
Or Resultant wave is the superposition of
fundamental and subsidiary waves.

Note:
Piano has larger no. of subsidiary
notes than flute.
So same note played by the two, can
be easily distinguished due to
difference in wave form

Sound quality can be defined as the degree of
accuracy with which a device records or emits the
original sound waves
The ordinary definition of vibrato is "periodic changes
in the pitch of the tone", and the term tremolo is
used to indicate periodic changes in the amplitude
or loudness of the tone.
vibrato - FM (frequency modulation) of the tone
tremolo - AM (amplitude modulation) of the tone

For my youtube videos: please visit -
SH vision youtube channel
or
xray diffraction series
SH Vision
Dr. Pius Augustine, SH College, KochiDr. Pius Augustine, SH College, Kochi

162
Appeal: Please Contribute to Prime Minister’s or Chief
Minister’s fund in the fight against COVID-19
Dr. Pius Augustine, Dept of Physics, Sacred Heart College, Thevara
we will
overcome
Thank You
http://piusaugustine.shcollege.ac.in
https://www.facebook.com/piustine
Please share
Dr. Pius Augustine, Asst. Professor, Sacred Heart College, Thevara, Kochi.

22 pius augustine sound, echo and resonance

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22 pius augustine sound, echo and resonance