lecture phy sound

7/29/2019 lecture phy sound

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Waves and Sound (part 1)

Lecture 2


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Outline

Types of Waves: Transverse and Longitudinal

Periodic Waves

The Speed of Wave in a String Producing a Sound Wave

Using a Tuning Fork to Produce a Sound Wave

Speed of Sound Sound Intensity

Decibel


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Wave Motion

A wave is the motion of a disturbance

Mechanical waves require

Some source of disturbance

A medium that can be disturbed

Some physical connection or mechanism though

which adjacent portions of the medium influence

each other

All waves carry energy and momentum


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Types of Waves Traveling Waves

Flip one end of a long ropethat is under tension andfixed at the other end

The pulse travels to the rightwith a definite speed

A disturbance of this type iscalled a traveling wave


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Types of Waves Transverse

In a transverse wave, each element that is disturbed

moves in a direction perpendicular to the wave

motion


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Types of Waves Longitudinal

In a longitudinal wave, the elements of the medium

undergo displacements parallel to the motion of the

wave A longitudinal wave is also called a compression wave


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Other Types of Waves

Waves may be a combination of transverseand longitudinal

Water waves are partially transverse and

partially longitudinal


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Periodic Waves

Periodic wavesconsist of cycles or patterns that areproduced over and over again by the source.

In the figures, every segment of the slinky vibrates insimple harmonic motion, provided the end of the

slinky is moved in simple harmonic motion.


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In the drawing, one cycle is shaded in color.

The amplitude A is the maximum excursion of a particle of

the medium from the particles undisturbed position.

The wavelength is the horizontal length of one cycle of thewave.

The period is the time required for one complete cycle.

The frequency is related to the period and has units of Hz, ors-1.

Tf1


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Speed of a Wave

v=

Is derived from the basic speed equation of distance/time

This is a general equation that can be applied to many

types of waves


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AM and FM radio waves are transverse waves consisting of

electric and magnetic field disturbances traveling at a speed

of 3.00 108 m/s. A station broadcasts AM radio waves

whose frequency is 1230 103 Hz and an FM radio wavewhose frequency is 91.9 106 Hz. Find the distance

between adjacent crests in each wave.

Example 1:


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Solution:

AM: m244Hz101230

sm1000.33

8

f

v

FM: m26.3Hz1091.9

sm1000.36

8

f

v


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A wave traveling in the positive x-direction is pictured in

Figure. Find the amplitude, wavelength, speed, and period

of the wave if it has a frequency of 8.00 Hz. In Figure,

x= 40.0 cm and y= 15.0 cm.

Example 2:


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Solution:

m0.150cm15.0 yA

m0.400cm.004 x

m/s02.3400.000.8 fv

s125.000.8

11

fT


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Speed of a Wave on a String

The speed on a wave stretched under sometension, F

mis called the linear density

The speed depends only upon the properties

of the medium through which the disturbancetravels


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Transverse waves travel on each string of an electric

guitar after the string is plucked. The length of each

string between its two fixed ends is 0.628 m, and the

mass is 0.208 g for the highest pitched E string and3.32 g for the lowest pitched E string. Each string is

under a tension of 226 N. Find the speeds of the

waves on the two strings.

Example 3:


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High E

sm826

m0.628kg100.208

N2263-

Lm

Fv

Low E

sm207

m0.628kg103.32

N2263-

Lm

Fv

Solution:


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A uniform string has a mass Mof 0.0300 kg and a length L of

6.00 m. Tension is maintained in the string by suspending a

block of mass m = 2.00 kg from one end .

(a) Find the speed of a transverse wave pulse on this string.

(b) Find the time it takes the pulse to travel from the wall to thepulley. Neglect the mass of the hanging part of the string.

Example 4:


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LM

mgFv

/

m

s0799.06.62

00.5)b( v

dt

Solution:

0)a( mgFF

m/s6.6200.60300.0

80.900.2v


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Interference of Waves

Two traveling waves can meet and pass through

each other without being destroyed or even

altered

Waves obey the Superposition Principle

When two or more traveling waves encounter each

other while moving through a medium, the resulting

wave is found by adding together the displacementsof the individual waves point by point

Actually only true for waves with small amplitudes


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Constructive Interference


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Destructive Interference


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Reflection of Waves

Fixed End

Whenever a travelingwave reaches a boundary,some or all of the wave is

reflected When it is reflected from

a fixed end, the wave is

inverted The shape remains the

same


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Reflected Wave Free End

When a traveling wave

reaches a boundary, all

or part of it is reflected

When reflected from a

free end, the pulse is not

inverted


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Sound Waves

Sound waves are longitudinal waves


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Producing a Sound Wave

Any sound wave has its source in a vibrating

object

Sound waves are longitudinal waves traveling

through a medium

A tuning fork can be used as an example of

producing a sound wave


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Using a Tuning Fork to Produce a

Sound Wave

A tuning fork will produce a

pure musical note

As the tines vibrate, they

disturb the air near them As the tine swings to the right,

it forces the air molecules near

it closer together

This produces a high density

area in the air

This is an area ofcompression


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Using a Tuning Fork, cont.

As the tine moves toward the

left, the air molecules to the

right of the tine spread out

This produces an area of lowdensity

This area is called a rarefaction


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Using a Tuning Fork, final

As the tuning fork continues to vibrate, a succession ofcompressions and rarefactions spread out from the fork

A sinusoidal curve can be used to represent thelongitudinal wave

Crests correspond to compressions and troughs torarefactions


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Categories of Sound Waves

Audible waves Lay within the normal range of hearing of the human ear

Normally between 20 Hz to 20 000 Hz

Infrasonic waves Frequencies are below the audible range

Earthquakes are an example

Ultrasonic waves Frequencies are above the audible range

Dog whistles are an example


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Speed of Sound, General

The speed of sound is higher in solids than in gases The molecules in a solid interact more strongly

The speed is slower in liquids than in solids

Liquids are more compressible

(liquid) (solid)


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Speed of Sound in Air

331 m/s is the speed of sound at 0 C

Tis the absolute temperature

or v= 331 + 0.6(T)where Tin degree Celcius (C)


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The Speed of Sound

Sound travels through

gases, liquids, and solids

at considerably different

speeds.


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A stone is dropped into a well. The splash is heard

3.00 s later. What is the depth of the well?

Example 5:


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Solution:

H = gt12 (a)

where t1 is the time the stone reach the water and H is

the depth of the well,

H = vt2(b)

Where v is speed of sound and t2 is the time the sound

travels.

But t1 + t2 = 3.00 s (c)Equate (a) and (b) and substitute in (c),

Solve for quadratic equation and H = 40.7 m


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An explosion occurs 275 m above an 867-m-thick ice

sheet that lies over ocean water. If the air

temperature is 27.00C, how long does it take the

sound to reach a research vessel 1250 m below theice? Neglect any changes in the bulk modulus and

density with temperature and depth.

(Use Bice = 9.2 109 N/m2.)

Example 6:


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Solution:

m/s327273

266331

273331

Tvair

s841.0327

275

air

airair

v

dt

m/s102.3917

102.9 39

Bvice

s27.0

3200

867

ice

iceice

v

dt

s815.01533

1250

water

waterwater

v

dt

s93.1815.027.0841.0 watericeairtotal

tttt


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Sound Intensity

Sound waves carry energy that can be used to do

work.

The amount of energy transported per second is

called the power of the wave.The sound intensity is defined as the power thatpasses perpendicularly through a surface divided by

the area of that surface.

A

PI

SI unit: W/m2


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12 x 10-5 W of sound power passed through the

surfaces labeled 1 and 2. The areas of these

surfaces are 4.0 m2 and 12 m2. Determine the

sound intensity at each surface.

Example 7:


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25

2

5

1

1 mW100.34.0m

W1012

A

PI

25

2

5

2

2 mW100.112m

W1012 A

PI

Solution:


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Intensity Level of Sound Waves

The sensation of loudness is logarithmic in the

human ear

is the intensity level or the decibel level of

the sound

Io is the threshold of hearing


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Intensity vs. Intensity Level

Intensity is a physical quantity

Intensity level is a convenient mathematical

transformation of intensity to a logarithmic

scale


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Various Intensity Levels


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A noisy grinding machine in a factory produces a

sound intensity of 1.001025 W/m2. Calculate

(a) the decibel level of this machine and

(b) the new intensity level when a second, identicalmachine is added to the factory.

(c) A certain number of additional such machines

are put into operation alongside these two

machines. When all the machines are running atthe same time the decibel level is 77.0 dB. Find

the sound intensity.

Example 8:


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Solution:

dB0.7010log101000.1

1000.1log10)a( 7

12

5

dB0.731000.11000.2log10)b(

12

5

12

1000.1

log10dB0.77)c(I

2570.7

12W/m1001.510

1000.1

I

I


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Audio system 1 produces a sound intensity level of

90.0 dB, and system 2 produces an intensity level of

93.0 dB. Determine the ratio of intensities.

Example 9:


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oI

IlogdB10

oI

I11 logdB10

oI

I22 logdB10

1

2

1

21212 logdB10logdB10logdB10logdB10

I

I

II

II

I

I

I

I

o

o

oo

1

2logdB10dB0.3I

I

0.210 30.0

1

2 I

I

1

2log0.30I

I

Solution:


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Spherical Waves

A spherical wave

propagates radially

outward from the

oscillating sphere The energy propagates

equally in all directions

The intensity is


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Intensity of a Point Source

Since the intensity varies as 1/r2, this is an inverse

square relationship

The average power is the same through any spherical

surface centered on the source To compare intensities at two locations, the inverse

square relationship can be used


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A small source emits sound waves with a power

output of 80.0 W.

(a) Find the intensity 3.00 m from the source.

(b) At what distance would the intensity be one-fourth as much as it is at r= 3.00 m?

(c) Find the distance at which the sound level is

40.0 dB.

Example 10:


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Solution:

2

2W/m707.0

00.340.80

4)a(

rPI

m00.6

4/707.04

0.80

'4

)b( I

Pr

28

0

00.4

0

W/m1000.110log10dB0.40)c(

II

I

I

8

2

2

12

1

2

22

1

2

2

2

1

1000.1

707.000.3

I

Irr

r

r

I

I

m1052.2 42 r

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