a brief overview on sound and vibration

8/6/2019 A Brief Overview on Sound and Vibration

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A Brief Overview on Sound and Vibration

Jagannath Sardar

(2008TTZ8165)

Department of Textile Technology

Indian Institute of Technology Delhi

New Delhi-16

September 20, 2008


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Content

.Page no

1. Introduction 3

2. Properties of Sound Waves 4

2.1 Reflection 4

2.2 Refraction 4

2.3 Interference 5

2.4 Diffraction 6

2.5 Doppler Effect 6

2.6 Intensity 6

3. Ultrasonic transducers 7

4. Loudness (dB) or the Sound Intensity Level (SIL) of a wave 8

5. Parameters of Sound Wave 9

5.1 Wavelength 9

5.2 Frequency 10

5.3 Amplitude 10

5.4 Speed 10

6. Equation of Progressive Wave 11

6.1 Damping of Vibration 12

6.2 Energy Dissipation by damping force 14

7. Conclusion 15

8. References 16


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1. Introduction

A sound wave can be defined as the pattern of disturbance caused by the movement of

energy traveling through a medium (such as air, water, or any other liquid or solid matter) as

it propagates away from the source of the sound.

The vibration can be described as some object that causes disturbs the particles in the

surrounding medium; those particles disturb those next to them, and so on. Sound travels

through the air (gas), water (liquid) or brick (solid), in fig. 1 shows as a pressurized

longitudinal wave. In a longitudinal wave the particle displacement is parallel to thedirection of wave propagation. And transverse wave the particle displacement is

perpendicular to the direction of wave propagation[1].

Fig. 1. Longitudinal waves

The compressing and expanding of the air produces differences in air pressure. The pressure

differences in the air move away from the drum surface like ripples in a pond, creating a

sound wave. This is how the drum produces a sound that we can hear.

To generate sound, it is necessary to have a vibrating source, such as the tuning fork shown

here. When the source vibrates, it displaces adjacent particles and molecules in the medium,

causing them to vibrate back and forth as well. Their vibrations cause more distant particles

to vibrate, and so on. The audible sound that we hear is made up of tiny vibrations of air

molecules, which are transmitted to our ears. This transmission of vibrations[Fig. 2],


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starting from the source and continuing from one molecule to the next, is how sound travels

through a medium[2].

It should be noted that air cannot sustain any form of shear stress so sound can only be

transmitted as a longitudinal wave.

Fig. 2. Sound wave Propagation

2. Properties of Sound Wave:

Sound wave has properties like

Reflection, Refraction, Interference and Diffraction[3].

2.1 Reflection:

Reflection of sound waves off of surfaces can lead to one of two phenomenons - an echo or

a reverberation. In fig. 3 shows reverberation often occurs in a small room with height,

width, and length dimensions of approximately 17 meters or less.

Fig. 3. Reflection of Sound wave

2.2 Refraction:


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2.4 Diffraction:

Diffraction[Fig. 6]: the bending of waves around small obstacles and the spreading out of

waves beyond small openings. Diffraction [4] involves a change in direction of waves as

they pass through an opening or around a barrier in their path.

Fig. 6. Diffraction

2.5 Doppler Effect:

The Doppler effect[Fig. 7] is a phenomenon observed whenever the source of waves is

moving with respect to an observer. The Doppler effect can be described as the effect produced by a moving source of waves in which there is an apparent upward shift in

frequency for the observer and the source are approaching and an apparent downward shift

in frequency when the observer and the source is receding[9].

Fig. 7. Doppler effect


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2.6 Intensity:

I as the rate at which energy E flows through a unit area A perpendicular to the direction of

travel of the wave[10].

Intensity is proportional to square of wave amplitude (remember energy in oscillator is

square of velocity and square of displacement).

3. Ultrasonic transducers:

A transducer is a device that transforms one form of energy into another, for example, a

microphone (sound to electric) or loudspeaker (electric to sound). In this experiment the

transducer is a "piezoelectric" crystal which converts electrical oscillations into mechanical

vibrations that make sound. The piezoelectric material contracts (or expands) a small

amount when a voltage is applied across the crystal[8]. The crystal has a natural resonance

frequency, like a bell, at which it will vibrate when struck. If the frequency of the voltage

applied to the piezoelectric crystal is the same as its natural frequency, the crystal will settle

into steady large amplitude oscillations that produce high intensity sound waves. The

oscillating frequency of the transducers you will use is near 40 kHz which is beyond what

can be heard by the human ear (about 20 kHz)[11].

In medical ultrasound the vibrating sources are "piezoelectric elements in an ultrasonic

transducer. The elements vibrate in response to applied electrical signals. The vibrating

motion of the transducer elements cause particles in adjacent tissues to vibrate, and the

ultrasonic vibrations travel through the tissue.

If the source vibrates continuously, a continuous sound is produced. In most cases in

ultrasound, the source vibrates briefly, producing a pulse of sound, which travels through the

tissue. After echoes are picked up, another pulse is sent, and so on.

).(Energy(E)

Area(a)Power(P)I)Intensity(

tatimeArea ==


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When a person speaks, vibrations of the vocal cords produce sound waves. Sound waves

usually travel faster through solids than through liquids or gases. Since they require a

medium to travel through, sound waves will not travel through a vacuum.

4. Loudness (dB) or the Sound Intensity Level (SIL) of a wave:

The decibel (dB) is used to measure sound level, but it is also widely used in electronics,

signals and communication. Fig. 8 Shows the dB is a logarithmic unit used to describe a

ratio. The ratio may be power, sound pressure, voltage or intensity or several other things[5].

The loudness of a sound, often referred to as the intensity, is dependent upon the amplitude

of the wave.

Fig. 8. Logarithmic unit

As amplitude increases, loudness increases. The intensity of a sound is expressed in units

called decibels. The intensity of a sound is related to the pressure on the eardrum. A sound

of 120 decibels is intense enough to cause pain in the ear. The softest sound that can be

heard is 0 decibels, while normal talking is about 65 decibels.

The pitch of a sound refers to its highness or lowness. The pitch of a sound depends on

frequency. The higher the frequency, the higher the pitch. The pitch of a sound changes

when the sound or the listener moves. When you listen to a siren on an approaching vehicle,

)log(100I

I=

a

P=I


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the pitch of the sound appears to increase as the vehicle approaches (pitch decreases for

vehicle going away). However, the pitch of the sound does not change. Instead, the number

of vibrations that reach your ear is changed when the source of the sound moves. Therefore,

the pitch appears to be higher or lower depending on whether the sound is moving toward or

away from you. This rise and fall of pitch due to relative motion between the observer and

the source of the sound is called the doppler effect.

The phon is a unit that is related to dB by the psychophysically measuredfrequency

response of the ear. At 1 kHz, readings in phons and dB are, by definition, the same.

The sone is derived from psychophysical measurements which involved volunteers

adjusting sounds until they judge them to be twice as loud. This allows one to relate

perceived loudness to phons. A sone is defined to be equal to 40 phons.

5. Parameters of Sound Wave:

Sound waves are characterized by the generic properties of waves, which are frequency,

wavelength, period, amplitude, intensity, speed, and direction (sometimes speed and

direction are combined as a velocity vector, or wavelength and direction are combined as a

wave vector).

5.1 Wavelength:

The transmitting and receiving transducer stands fit over, and can slide along, a meter stick.

With both transducers fixed in position, the two sinusoidal traces on the scope are steady.

What happens to the scope trace from the receiving transducer when you move the receiving

transducer away from the transmitting transducer?

Measure the wavelength by slowly shifting the receiving transducer a known distance

away from the transmitter while noting on the oscilloscope screen by how many completecycles of relative phase the wave pattern shifts. Don't choose just one cycle, but as many

cycles as can conveniently be measured along the meter stick.

Use the measured period of ultrasonic oscillations from Part 1 and the wavelength from

Part 2 to compute the speed of sound through air. The oscillation period measured with the

scope sweep calibration is more accurate than the frequency readings on the signal


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generator. Compare your computed value with the standard value of 344 m/s for dry air at

20 C temperatures[12].

5.2 Frequency:

Frequency is a measure of the number of occurrences of a repeating event per unit time. The hertz (symbol: Hz) is a measure of frequency, informally defined as the number of

events occurring per second. It is the basic unit of frequency in the International System of

Units (SI), and is used worldwide in both general-purpose and scientific contexts. Hertz can

be used to measure any periodic event.When the loudness of a sound wave changes, so doesthe amount of compression in airwave that is traveling through it, which in turn can be

defined as amplitude[13].5.3 Amplitude:

Amplitude is the magnitude of change in the oscillating variable, with each oscillation,

within an oscillating system. For instance, sound waves are oscillations in atmospheric

pressure and their amplitudes are proportional to the change in pressure during one

oscillation. If a graph of the system is drawn with the oscillating variable as the vertical axis

and time as the horizontal axis then the amplitude may be measured as the vertical distance

between points on the curve. Peak-to-peak amplitude is to measure it between peak andtrough[14].

Displacement Amplitude: ............. (1.1)

Peak-to-peak amplitudes can be measured by meters with appropriate circuitry, or by

viewing the waveform on an oscilloscope, or by an accelerometer5.4 Speed:

The speed of sound depends on the medium through which the waves are passing, and is

often quoted as a fundamental property of the material. In general, the speed of sound is

proportional to the square root of the ratio of the elastic modulus (stiffness) of the medium

to its density[15].

P=C

c

PA 0

=


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Speed of the Sound ............. (1.2)

The study of sound and vibration are closely related. Sound, or "pressure waves", are

generated by vibrating structures; these pressure waves can also induce the vibration of

structures. Sound = vibrations of matter (sound and other longitudinal waves require particle

of matter to travel through). The closer the molecules are together the louder the sound.

Speed of sound in air at 0 C = 331 m/s or about 1100 ft/s (speed varies with temperature, as

temperature increases the speed increases).

For every degree above 0 C multiply by 0.6 / t example: 35 C = 331 m/s + (0.6 35 C) =

352 m/s

6. Equation of Progressive Wave:

The simplest type of wave is the one in which the particles of the medium are set into simple

harmonic vibrations as the wave passes through it. The wave is then called a simple

harmonic wave[16].

Where A is the amplitude,is the angular frequency of the wave. Consider a particle P at a

distance x from the particle O on its right. Let the wave travel with a velocity v from left to

right. Since it takes some time for the disturbance to reach P, its displacement can be written

as

Whereis the phase difference between the particles two Positions.

We know that a path difference ofcorresponds to a phase difference of2radians. Hence a

path difference of x corresponds to a phase difference of

Substituting equation (1.5) in equation (1.4) We get,


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Similarly, for a particle at a distance x to the left of 0, the equation for the displacement is

given by

Then we can write the general equation of the progressive wave as

)(2sin xCtaY

=

Where, a = Amplitude

t = 1/n (frequency)

= wave length

6.1 Damping of Vibration:

The vibration hampered from within and without and of gradually diminishing amplitude arecalled resisted or damped vibration

When the oscillator has damping, the oscillator loses energy during each cycle, and both the

position and velocity decrease in amplitude as time proceeds. In Fig. 9, graphs of position

versus time and velocity versus time display an amplitude envelope which decreases

exponentially.


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It can be assumed that the frictional force is proportional to the velocity of the vibration,

and, in fact, this assumption approximates very closely to actual conditions.

In such cases we speak of viscous damping[6, 17].

Fig. 9. Damping propagation of Sound Waves

The proportionality factor is known as the damping constant (r)

The equation of motion for a damped free vibration is thus:

02

2

=++ kxdt

dxr

dt

xdm

Where x = Cet

r = retarding force per unit velocity

k = displacement per unit forceFrom the equation we can fine out general equation as m2 + r+ k = 0

And we can find out of the values of

i.e. =

e-t

-e-t

+

-

x

)4

(2

2

2

m

k

m

r

m

r+


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6.2 Energy Dissipation by damping force:

This will supply to the system just as much energy per vibration as there is lost in vibration

energy as given by the equation[7,18], the amplitude is being maintained at a constant value

of x0

We know

2

00

2

0

000

2

0

2

0

00

2

0

2

0

2

0

000

2

0

0

0

2

12sin

4

1

)(.sin

)(cos.sin

xr

ttrx

tdtrx

tdtrxdxkE

t

r

+

=

txx000

sin=


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7. Conclusion:

Acoustics is defined as the scientific study of sound which includes the effect of reflection,refraction, absorption, diffraction and interference. Sound can be considered as a wave

phenomenon. A sound wave is a longitudinal wave where particles of the medium are

temporarily displaced in a direction parallel to energy transport and then return to their

original position. The vibration in a medium produces alternating waves of relatively dense

and sparse particles compression and rarefaction respectively.

The resultant variation to normal ambient pressure is translated by the ear and perceived as

sound. A simple sound wave may be described in terms of variables like: Amplitude,

Frequency, Wavelength, Period and Intensity.

Amplitude refers to the difference between maxima and minima pressure. Frequency of a

wave is measured as the number of complete back-and-forth vibrations of a particle of the

medium per unit of time. A commonly used unit for frequency (f) is the Hertz (abbreviated

Hz). The wavelength () of a wave is the distance which a disturbance travels along the

medium in one complete wave cycle. Since a wave repeats its pattern once every wave

cycle, the wavelength is sometimes referred to as the length of the repeating patterns. The

term period can be defined as the time required for the completion of one cycle of wave

motion. The intensity of a sound wave is defined as the average rate at which sound energy

is transmitted through a unit area.


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8. References:

1.

http://www.glenbrook.k12.il.us/gbssci/phys/Class/sound/u11l1b.html2. http://www.kemt.fei.tuke.sk/Predmety/KEMT320_EA/_web/Online_Course_on_Acoustic

s/index_acoustics.html

3. http://hyperphysics.phy-astr.gsu.edu/Hbase/sound/interf.html

4. http://hyperphysics.phy-astr.gsu.edu/hbase/sound/diffrac.html

5. J.Acoust.Soc.Am. 6:59; Robinson, D.W. and Dadson, R.S.(1956) Br. J. Appl. Phys. 7:166

6. Introduction to study of Mechanical vibration, G.W. Van Santen. Pp36-37

7. Introduction to study of Mechanical vibration, G.W. Van Santen. Pp 42-43

8. www.soundimages.com

9. www.windows.ucar.edu/tour/link=/earth/Atmosphere/tornado/doppler_effect.html

10. www.physics.rutgers.edu/~jackph/2005s/PS04.pdf .

11. www.directindustry.com/industrial-manufacturer/ultrasonic-transducer-72169.html

12. www.vibrantwavelength.com/home.htm

13. www.imdb.com/title/tt0186151

14. www.fontbureau.com/fonts/Amplitude

15. www.mathpages.com/home/kmath109/kmath109.htm

16. www.greenandwhite.net/~chbut/new_page_12.htm

17. Sound Wave, C.R.D.G, pp. 421-424

18. Advance Acoustics, P. Roychowdhury, pp. 20-28


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a brief overview on sound and vibration

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