lec28-soundwaves.ppt 773KB Jun 23 2011 10:24:00 AM

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Physics 211 – lecture 28: Sound Waves

Sound Waves -

mechanical longitudinal waves

 Sound waves come from periodic pressure variations moving along in a substance.

increasing f

decreasing



infrasonic audible ultrasonic

20Hz 20kHz

Sound Spectrum – three classes of sound waves

C T s

m

air C

v



331

1



_273

Sound Speed

 Sound speed IN AIR at room temperature (20 C) is : _____________

 Sound speed equation (IN AIR only):

Note – speed  as density  and speed  as elasticity (stiffness) 

property

inertial

property

elastic

density

modulus

bulk









2

Wave Equation for Sound

Recall

y

(

x

,

t

)



A

sin(

kx





t

)

For transverse, we now have longitudinal

)

sin(

)

,

(

x

t

s

_max

kx

t

s







Max longitudinal displacement

Or in terms of pressure

)

sin(

)

,

(

x

t

P

_max

kx

t

P











3

Sound Intensity

Intensity

= power (or energy transfer rate) divided by area

Units: W/m2

Inverse Square Law:

2 12 0 0

10

I

where

log

10

m

I

I

_{ W}



















2 1 2 1 2















R

R

I

I

Decibels =

measure intensity relative to the minimum intensity we can hear. The decibel is a __________ scale. Our hearing works on this scale.

10 dB increase  increase by factor of 10 in intensity

20 dB increase  increase by factor of 100 in intensity 30 dB increase  increase by factor of 1000 in intensity

and so on…

Decibel Equation:



s



I

v

r

A

I





₂



₂1 _max 2



4







4

Doppler Effect

Doppler Effect

The Doppler effect describes a change in frequency (pitch) of sound waves due to a moving source or moving observer. Example: train approaches

with high pitched whistle, passes by, and pitch decreases.

Source moves: toward observer ________away from observer________

Observer moves: toward source _______away from source _________

5

Doppler Effect in Light

• Red Shift

- light from objects receding (moving away) from us is

shifted to the red side of the spectrum

• Blue Shift

- light from objects approaching (moving toward) us is

shifted to the blue side of the spectrum

s s

o

f

v

v

v

f

















s o

o

f

v

v

v

f











 



v_o = observer velocity f_o = observed frequency v_s = source velocity f_s = source frequency v = speed of sound

+ = moving away - = getting closer

+ = getting closer - = moving away

Doppler Effect Equations

:

6

Example (Doppler Effect):

A storm is formulating with winds of up to

150km/hr. A Doppler radar device is monitoring the storm by sending out a 35MHz signal? What frequency will bounce back to the station if the storm winds are

A) approaching? B) receding ?

Given Path Want Conversions/Equations

MHz

f

v

x

v

s hr km o s m

35

150

10

3

8







o s

o

f

f

v

v

hr

s

m

km







,

,

MHz

f

_o



?

s o

f

v

v

v

f

m

km

s

hr











 







1000

1

3600

1

83MHz 34.9999951 6MHz 35.0000048                                                        MHz x x f v v v f MHz x x f v v v f s m s hr km m hr km s m s m s m s o o s m s m s m s o o 35 10 3 6 6 . 41 10 3 : receding 35 10 3 6 6 . 41 10 3 : g approachin 6 6 . 41 3600 1 1000 150 8 8 8 8

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Example: Ch17 # 3

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Example: Ch17 # 16

Cu bar is at 99.5% of Y=13N/m^2. 500Hz sound wave is then transmitted. a) Find displacement amplitude required to

break bar

9

Example: Ch17 # 34

Firework explodes 100m up. Observer directly under explosion hears average intensity of

0.07W/m^2 for 0.2s.

10

Example: Ch17 # 38

Fetus ventricular wall moves in simple

harmonic motion with amplitude 1.8mm at 115 beats per minute. Detector on mother procudes sound at 2x10^6Hz which travels through

tissue at 1.5km/s. Find

a) Max linear speed of heart wall