lesson sound waves

8/13/2019 Lesson Sound Waves

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Lesson 16, 17 and 18: Sound Waves

Contents:

Superposition and Interference of Sound Waves

Standing Waves

Sound Waves

Superposition of Harmonic Waves

What happens when two waves collide? They ADD together! We say the waves are

superposed. For example when two sets o waves pass through one another the wave

crests rom one set reinorce the wave crests rom the other set to orm supercrests whenthey meet. "n other hand when a wave crest meets a wave trough the resultant is that

they cancel one another out.

Constructive Interference#rest $ crest % supercrest

Trough $ trough % supertrough

Destructive Interference

#rest $ trough % &ero

Principle of superposition

The total displacement at a point = the sum of individual displacements at that point.

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#onsider two harmonic wavesAandBmeeting atx = . They have same

amplitudes their angular re(uency is dierent. The displacement versus time or

each is shown )elow*

Wave A

Wave +

#om)ined wave

Super position of waves experiment

,tudents use two power supplies a signal generator an ampliier-speaer and a #/" tosimulate the superposition o two waves. The principle o superposition is discovered and

applied to a theoretical situation when the waves have slightly dierent re(uencies and

would produce )eats. 0redictions are made a)out the )eat re(uency and the re(uency othe note produced )y the waves. This is checed with the e(uipment.

+eat re(uency %f'1f2

Cathode ra! oscilloscope" # po$er supplies #% ' AC" ( signal generators" Amplifier

$ith spea)er

CONS!"C#$%

#N%!&%!%NC%

'%S!"C#$%

#N%!&%!%NC%

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)ac and orth. ,uch patterns are only created within the medium at speciic re(uencies

o vi)ration. These re(uencies are nown as harmonic re(uencies or merely harmonics.

The term harmonic has a precise meaning 1 that o an integer 5whole num)er6 multiple othefundamental fre*uenc!o a vi)rating o)7ect. At any re(uency other than a harmonic

re(uency the intererence o relected and incident waves results in a distur)ance o the

medium which is irregular and non1repeating. ,tanding waves occur in vi)rating stringsand in air columns.

The lowest re(uency produced )y any particular instrument is nown as the fundamental

fre*uenc!.The undamental re(uency is also called the irst harmonic o the instrument.

The speed o standing wave is same or all the all 8armonics o a single string. 8ow ever

the re(uency and wavelength changes.

Wavelength o the standing wave % 2 x length o the string % wavelength o 'st harmonic

8armonic num)er harmonic num)er

n= &+n

Fre(uency o a standing wave % harmonic num)er x re(uency o 'st

harmonic

fn= n f&

&actors t)at affect t)e fundamenta* fre+uenc -f. of a vi/ratin( strin(

fis proportional to '-length

,alving the length dou-les the fre*uenc!

f is proportional to Tension

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Tension increased four times dou-les the fre*uenc!

fis proportional to'- lengthunitperstringtheofmass ......

,eav! string vi-rates at lo$er fre*uenc!

Sound Waves

,ound is deined as arange of compression%$ave fre*uencies to $hich the human ear issensitive.

:nrasonic )elow 2; 8& 58uman ear cannot detect6

,onic 2; 8& < 2;;;; 8& 5Audi)le ,ound6

=ltrasonic a)ove 2;;;; 8& 58uman ear cannot detect6

Nature of Sound waves

,ound is produced )y vi)rating o)7ects such as the sin o a drum a string o a

guitar the air column o the trumpet.

,ound waves need a material to travel through.

,ound waves can travel through solids li(uids and gases.

,ound waves are longitudinal waves

In longitudinal $aves the oscillations ta)es place in the direction of $ave travel.

The ollowing diagram shows how the )acward and orward movement o a one1end

ixed sliny spring produces a longitudinal wave.

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The diagram )elow shows how the sound produced )y a speaer is transmitted to the

)rain.

&re+uenc and 0itc)

Dierent re(uency sound dierent to the ear. 8igh re(uencies are heard as note said to

)e as high pitch. ow re(uencies are heard as notes to )e low pitch.

im/er and Overtone

When same note is played on dierent musical instruments the sound (uality or tim)er is

dierent. This is )ecause o overtones which are weaer re(uencies added to the

undamental re(uency. The term overtone is used to reer to any resonant fre*uenc!

a)ove the undamental re(uency 1 an overtone may or may not )e a harmonic. 8armonicis an overtone with a re(uency that o an integer 5whole num)er6 multiple o the

fundamental fre*uenc!.

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Speed of Sound

The speed o sound varies considera)ly depending on the material through which the

waves are traveling.

,peed sound in air 44; m-s 5dry air at ;o#6

,peed o sound in water '9;; m-s 5at ;o#6

,peed o sound in concrete >;;; m-s

,peed o sound does not depend on the pressure

The speed o sound increases with temperature

,peed o sound can )e calculate using the ollowing ormula

,peed % re(uency x wavelength

v %f

easurin( speed of sound usin( ec)o met)od

choes5 relection o sound6 can )e used to mae estimate o speed o sound in air. Astudents stands ';; m rom high wall and clap hands together at such a rate that each clap

coincides with the echo o the one )eore. The time or ' clap can )e calculated as )elow

and then speed o sound can )e ound.

Time or ' clap 5t6 % total time-total num)er o claps

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,peed o sound is % distance traveled )y sound % 2d

Time or ' clap t

easurin( t)e speed of sound usin( dou/*e /eam osci**oscope

#onnect two microphones to a dou)le1)eam oscilloscope. ,et up a signal generator and

loudspeaer to give sound waves o re(uency ' 8&. 5Their wavelength is thus a)out ;.4

m.6

0lace one microphone close to the loudspeaer and o)serve its trace. 0lace the secondmicrophone urther rom the loudspeaer in the same straight line. ")serve its trace.

Cove it )ac and orth noting the changing phase dierence )etween the two traces as

you move through the sound waves.

Ceasure the wavelength 5with a ruler6 )y inding how ar the microphone is moved

)etween ad7acent positions where the signals are in phase. #alculate the speed o sound.

ote that i you donEt have two microphones you can lin the signal generator and

loudspeaer to one input. Then ind two consecutive positions o the microphone whichare in antiphase with the signal. Antiphase is easy to see when the traces are

superimposed on the screen.

: you donEt have a dou)le )eam oscilloscope wait until a lesson on standing waves and

then use a single )eam one.

2mp*itude, Loudness and #ntensit

Amplitude is the maximum distance a loudspea)er cone moves -ac)$ards or for$ards

from its rest position.: the amplitude o the loudspeaer cone increases the intensity othe sound increases so the sound )ecomes louder.


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Intensit! of the sound $ave is a measure of the $ave energ! passing ever! second

through each s*uire meter at right angles to its path. The sound intensity 5outward6 is

inversely proportional to the s(uare o the distance rom the point source.

:ntensity % nergy % 0ower

Time x Area Area

=nit o intensity is W-m2

This faintest sound $hich a human ear can detect is )no$n as the threshold of hearing.

The aintest sound which the typical human ear can detect has an intensity o 'G';1'2W-m2.

)e 'eci/e* sca*e

,ince the range o intensities which the human ear can detect is so large the scale which

is re(uently used )y physicists to measure intensity is a scale )ased on multiples o ';.This type o scale is sometimes reerred to as a logarithmic scale. The scale or measuring

intensity is the deci-el scale.

Source Intensity

# of TimeGreaterThan TOH

IntensityLevel

Threshold of Hearing (TOH) 1*10-12W/m2 100 0 dB

Rustling Leaes 1*10-11

W/m2

101

10 dB

Whis!er 1*10-10W/m2 102 20 dB

"ormal #onersation 1*10-$W/m2 10$ $0 dB

Bus% &treet Traffi' 1*10-W/m2 10 0 dB

a'uum #leaner 1*10-+W/m2 10, ,0 dB

Large Or'hestra $.*10-.W/m2 10 , , dB

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Walman at aimum Leel 1*10-2W/m2 1010 100 dB

3ront Ro4s of Ro' #on'ert 1*10-1W/m2 1011 110 dB

Threshold of 5ain 1*101W/m2 101. 1.0 dB

ilitar% 6et Taeoff 1*102W/m2 101+ 1+0 dB

7nstant 5erforation of8ardrum 1*10+W/m2 101$ 1$0 dB

!efraction of Sound

: the air a)ove the earth iswarmer than that at the

surace sound will )e )ent

)ac downward toward thesurace )y refraction.

,ound propagates in all directions rom a point source. ormally only that which is

initially directed toward the listener can )e heard )ut reraction can )end sounddownward. ormally only the direct sound is received. +ut reraction can add some

additional sound eectively ampliying the sound.

Distance traic and trains oten sound much closer and louder at night )ecause oreraction o sound waves.

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'iffraction of Sound

Diffraction the -ending of $aves around small/ o-stacles and the spreading out of$aves -e!ond small/ openings.

G small compared to the wavelength

,ound can )e heard around corners and around )arriers involves )oth diraction and

relection o sound. Diraction in such cases helps the sound to I)end aroundI the

o)stacles. The act that diraction is more pronounced with longer wavelengths impliesthat you can hear low re(uencies around o)stacles )etter than high re(uencies as

illustrated )y the example o a marching -andon the street. Jou may also perceive

diraction to have a dual nature since the same phenomenon which causes waves to)end around o)stacles causes them to spread out past small openings.

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The long wavelength sounds o the )ass drum will diffractaround the corner more

eiciently than the more directional short wavelength sounds o the higher pitched

instruments.

!ef*ection of Sound and !ever/eration

8ard surace such as walls will relect sound waves. When you hear an echo you are

hearing a relected sound a short time ater the original sound. :n echo1sounding

e(uipment itted to some )oats sound pulses are relected rom the sea )ed and echo timeis used to measure depth o water under the )oat.

During 0ever-eration" the echo time is ver! short and echoes overlap and sound seems

to -e prolonged

!ef*ection from Concave Surface

Any concave surace will tend to ocus the sound waves which relect rom it. This isgenerally undesira)le in auditorium acoustics )ecause it produces a Ihot spotI and taes

sound energy away rom surrounding areas. ven dispersion o sound is desira)le in

auditorium design and a surace which spreads sound is preera)le to one which ocusesit.

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2ctivities t)at can /e done in t)e c*ass

'. ,peed o sound using #/".

2. +eat using 2 signal generators and 2 speaers close to each other

4. :ntererence o 8armonic waves using a #/"

9. #alculate the speed o standing waves produced in one1end closed tu)e using a signal

generator.

0ractice Kuestion

Core

'. What type o wave motion is sound?

2. What is the dierence )etween transverse waves and longitudinal waves?

4. Why is it possi)le to hear round corners?

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9. What happens to the speed o sound in air when 5i6 air pressure rises 5i6 temperature

rises?

>. What are standing waves?

@. What happens to the pitch o a note when the re(uency is raised?

B. What is the dierence )etween overtones and harmonics?

. What are the actors aecting the undamental re(uency o a vi)rating string?

H. What is a tim)er in sound?

';. Live the re(uency ranges o 5i6 inrasonic 5ii6 sonic and 5iii6 ultrasonic

''. Deine the ollowing terms

5i6 :ntensity

5ii6 Amplitude

'2. What is the threshold o hearing?

'4. xplain what deci)el scale is?

'9. With the help o 4 setches explain the 'st 2ndand 4rdovertones o a vi)rating string.

'>. What is relection o sound?

'@. What is diraction o sound?

'>. xplain what rever)eration is.

'B. With the help o simple setches explain the meaning o constructive intererenceand destructive intererence.

Structured 3uestions

'. A student stands >; m away rom a tall wall and claps 2 )loc o wood >; times in away so that sound coincides with the echoes. 8is riend measures the time or >; claps

and inds it to )e '>s.

a. #alculate the time taen or ' clap.

). What is the total distance traveled )y the sound? 8ow do you now that?

c. #alculate the speed o sound in the air.

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'H. A sound source has an intensity o 1*10-+W/m2at 1m from the sound sour'es Find the

intensity o the sound at a distance o 4m.

2;. A undamental re(uency o sound produced )y a vi)rating string o a piano is 2@'.@48&. #alculate the re(uency o the 5i6 2ndharmonic 5ii6 4rdharmonic and 5iii6 9thharmonic.

#ircle around the note name in the diagram )elow or each answer.

2'. A student connects a speaer to signal generator. 8e increases the re(uency o thesound produced on the signal generator eeping the speaer over one1end1opened pipe

and hears a loud sound at a re(uency o 99; 8&.

a6 Why he hears a loud sound at a particular re(uency not any other lower re(uency?

)6 What do you call this re(uency o the standing waves produced in the tu)e?

c6 What is the wavelength o the standing wave i the length o the pipe is ;.';m?

d6 #alculate the speed o standing wave produced in the pipe.

22. "ne loudspeaer emits a note o re(uency 2;; 8&. A second loudspeaer emits an

e(ually loud note o re(uency 2;> 8&.

5i6 What would you hear when you stand near the loudspeaers?

5ii6 What happens i the re(uency o the second loudspeaer is lowered to 2;2 8& and

then 2;; 8&?

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5iii6 #alculate the )eat re(uency when the re(uency o the second speaer is 2;> 8&.

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lesson sound waves

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