Sound Waves

By : Dr. Nitin Oke.

Waves Electromagnetic (do not need medium) Mechanical (needs medium) elastic, posses inertia , gives minimum resistance Longitudinal Transverse Safe Hands Ripple

Longitudinal Transverse Ripple Comp.& rare. Crest & Turf P,



changes



Need volume elasticity stress changes



Need shape elasticity Pass through S,L,G Pass through S or L surface Safe Hands

Longitudinal Wave

wave particles vibrate back and forth along the path that the wave travels.

Compressional Wave

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Waves transfer energy without transferring matter.

Frequency= number of waves/time Safe Hands

Water Waves

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Sound waves

• Sound energy is transferred by Longitudinal waves • Sound waves can not be polarized • Velocity of longitudinal waves is given by Newton as

E ρ

• Newton assumed propagation as isothermal process and then bulk modulus for gas in isothermal condition is P thus speed is

P ρ

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• When values are substituted the theoretical value is less (280m/s) than the observed value(331m/s).

• Laplas corrected that propagation of sound is not isothermal it is adiabatic thus E =



P then value matches with observed value.

• Thus v =



(



P/



) Safe Hands

• Medium air (20 o C) air (0 o C) water (25 o C) sea water diamond iron copper glass velocity m/sec 343 331 1493 1533 12000 5130 3560 5640

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Factors affecting the speed of sound

• Effect of pressure: There is no effect of change in pressure on speed of sound • Effect of Temperature : Speed of sound is proportional to square root of temperature.( if medium is same) • Effect of molecular weight of medium: Speed of sound is inversely proportional to square root of molecular weight .( if temperature is same) Safe Hands

Factors affecting the speed of sound

• Effect of density: Speed of sound is inversely proportional to square root of density of medium • Effect of humidity: When humidity increases the amount of water vapors in air increases as water vapors are of less density than of air the effective density of humid air decreases. Hence velocity of sound increases in humid air.

• Velocity of sound is more in summer days due increase in temperature.

• Velocity of sound is more in rainy days due increase in humidity.

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Transverse waves

• Crests: Highest part of a wave • Troughs : The low points of the wave

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Reflection of wave

T- wave L- wave From rigid surface From free surface



phase =

 

phase = 0 C T



T



C C T



C



T From rigid surface From free surface



phase =

 

phase = 0

C 

R R

 C

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C  

R

C

R

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Ultrasound

sound waves with frequencies above the normal human range of hearing. Sounds in the range from 20-100kHz

Infrasound

- sounds with frequencies below the normal human range of hearing.

Sounds in the 20-200 Hz range Safe Hands

Analytical representation of sound waves

• In general progressive waves are represented by F(v-xt) • If y represents displacement of a particle of medium at a distance x and at time t then we may have an equation y = A sin (



t-



) = A sin (



t- (2



x/t)) Safe Hands

y



Asin

ω

t



2

π

x

λ

y



Just substitute n= 1/T and don’t forget n



=V w x

λ

y



A sin2

π

t T x

λ

y



n



Asin

  

2

π

nt



2

π

x

λ

Or Should it be just

   

y



Asin2

π 

nt



x

λ

Safe Hands y



Asin2

π

n

 

t



x V w

 

Principle of superposition of waves • When two or more waves traveling through a medium arrive at a point of the medium simultaneously, each wave produces its own effect (displacement) at that point independently of the others and the resultant effect (displacement) at that point is equal to the vector sum of the individual displacements of all the waves. Let Y 1 , Y 2 , Y 3 - - - - - be the individual displacements due to each wave.

When all the waves acting simultaneously then the resultant displacement y is given by Y = Y 1 + Y 2 + + Y 3 + - - - - Safe Hands

Three cases of superposition of waves (i) Interference of waves : Two waves of the same frequency traveling along the same path with the same speed in the same direction.

This gives rise to the phenomenon of interference of waves.

There are two types of interferences:(a) Constructive interference (b) Destructive interference Safe Hands

Interference

• the result of two or more sound • waves overlapping

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Three cases of superposition of waves (ii) Stationary waves: Two waves of the same amplitudes and same frequencies waves.

traveling along the same path with the same speed in the opposite directions. This gives to the phenomenon of stationary Safe Hands

Three cases of superposition of waves (iii) Beats: Two waves of slightly different frequencies traveling along the same path with the same speed in the same direction.

This gives rise to the phenomenon of beats.

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Theory of beats

• When two sound waves of same amplitude but slightly different frequencies traveling along the same path with the same speed in the same direction, the resultant amplitude thus intensity is alternately maximum and minimum. This phenomenon is called beats. • The maximum intensity of sound is called “waxing” and minimum intensity of sound is called “waning.” • One waxing and one waning constitute one beat.

• The time interval between two successive waxing or waning is called the period of beats. The number of beats per second is called the frequency of beats.

• The frequency of beats is equal to the difference in the frequencies of the two sound waves.

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Analytical approach to beats

• If two sound waves sound waves producing beats are given by equations • Y 1 = Asin2



n 1 t & • Y 2 = Asin2



n 2 t then their resultant can be obtained by using the relation • sinA + sinB = 2(cos(A-B)/2).(sin(A+B)/2) • Y = {2A (cos



(n 1 – n 2 )t)}.sin2



((n 1 sound is of frequency (n 1 minima with frequency ( n 1 + n amplitude is varying between maxima and – n 2 2 ).

+ n 2 )/2)t. this )/2 such that its Safe Hands

If this frequency means beat frequency is more than 20 Hz then we can not distinguish between the maxima and minima thus a sound of frequency (n 1 + n 2 )/2 will be heard, this is called as difference tone.

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Application of beats

• (1) The phenomenon of beats is used to determine the frequency of turning fork.

– Remark – (i) when the prongs of a turning fork are loaded with wax, the frequency of fork decreases.

– (ii) When the prongs of turning fork are filled, the frequency of fork increases.

• (2) The phenomenon of beats is used to tune musical instruments: • (3) The phenomenon of beats is applied in detection of harmful gases like methane in a mine • (4) To produce intermediate frequency Safe Hands

Doppler’s effect

• The apparent change in the pitch (or frequency) of sound due to the relative motion between source of sound and observer (listener) is called Doppler effect.

• The frequencies are related by n a



V



V 0 V s

 

n upper signs indicate relative approach, lower signs relative recession. Safe Hands

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Applications of Doppler effect Doppler’s effect is used in –



The working of RADAR ( RA dio D etection A nd R anging) an equipment is used to detect aero plane along with its speed.

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is used to determine the speed of stars and planets.

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in the working of SONAR ( SO und waves N avigation A nd R anging) the equipment is based on Doppler effect.This equipment is used to detect submarines and its speed

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is used to determine the speed of rotation of the Sun.

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Is used to study motion of galaxies

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Function and state of heart valves

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Used by bats, Scorpios to detect and catch the food Safe Hands

Musical Sound • Sound produced by periodic vibrations is called a musical sound.

• When sound is produced by non periodic vibrations it is called as noise.

• Musical interval : The musical interval between the two notes is defined as the ratio of the frequency of higher note to the frequency of lower note. Some slandered ratios are as follows.

–Unison: Here the musical interval = 1or N 2 =N 1 –Octave: Here the musical interval = 2 or N 2 = 2N 1 Hence N 2 is the octave of N 1 .

–Major tone: Here the musical interval =9/8 N 2 = 9N 1 /8 –Minor tone: Here the musical interval = 10/9. N 2 = 10N 1 /9 –Semi tone: Here the musical interval = 16/15. N 2 = 16N 1 /15 Safe Hands

Words used in musical sound

• (i) Loudness (L): It is the sensation received by the ear due to intensity of sound. Loudness depends upon the sensitivity of the listener ear. Therefore, loudness of a sound of a given intensity may be different for different listeners.

• Loudness (L) of sound increases with intensity of sound according to Weber-Fechner law in physiology.

• According to this law, L measured in “Bell”



log I,L=K log I, where K is a constant. This relation is known as Weber- Fecher relation. Loudness is Safe Hands

Words used in musical sound

• (ii) Pitch: It is the characteristic of musical sound by which a shrill (sharp) sound can be distinguished from a grave (or flat) one, even though the two sounds may be of the same intensity.

• Pitch means non quantitative frequency.

– (i) The buzzing of bee has high pitch but low loudness while the roar of a lion has large loudness but low pitch.

– (ii) Due to hormones usually the pitch of female voice is higher than her male.

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Words used in musical sound

Low pitch

high intensity High pitch

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Words used in musical sound

• (iii) Quality (or Timbre): It is the characteristics of musical sound, which enables us to distinguish between two sounds of the same pitch and loudness. A musical instrument vibrates with many frequencies at same time, the lowest frequency is called as fundamental, and multiples are called as overtones. The quality is determined by the number of overtones and their relative intensities.

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Time

V

V V

L W

  

(n

1



beat

Quick revision of sound waves

Time Y V

n

P

 ω γ λ

n

ρ

k

P



of Asin(

ω

stress

ρ ω

of

ω γ

A M beats frequency

  

and

πn

frequency T (n

1

Y m ( t (



n ).(



( ( n t beat

γ

2

t

 

1.

) t t M t t



T

1.

0

 

e



2 Mg m

2

2

  2

x

 λ  π π

)

λ λ ) 

2 x

λ

x

λ π λ

1

) ) ) ) ) )

n 2 RMS )

x Mg

π

r

2

ρ

)

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