physics 231 introductory physics i
TRANSCRIPT
![Page 1: PHYSICS 231 INTRODUCTORY PHYSICS I](https://reader030.vdocuments.us/reader030/viewer/2022012708/61a88e52c546ea326e6fad3a/html5/thumbnails/1.jpg)
PHYSICS 231
INTRODUCTORY PHYSICS I
Lecture 23
![Page 2: PHYSICS 231 INTRODUCTORY PHYSICS I](https://reader030.vdocuments.us/reader030/viewer/2022012708/61a88e52c546ea326e6fad3a/html5/thumbnails/2.jpg)
• Speed of sound in fluid
(for solid, replace )
• Intensity
• Intensity Level - dB
• Spherical Waves
Last Lecture -Sound
v =B
!
! = 10 log10I
Io
I = I010! /10
I =P
4!r2
!
B"Y
!
I =P
A
!
I0
=10"12W/m
2
![Page 3: PHYSICS 231 INTRODUCTORY PHYSICS I](https://reader030.vdocuments.us/reader030/viewer/2022012708/61a88e52c546ea326e6fad3a/html5/thumbnails/3.jpg)
Doppler Effect, Moving Observer
Fig 14.8, p. 435
Slide 12
Towards source:
Away from source:
ƒ' = ƒv + v
o
v
!"#
$%&
ƒ' = ƒv ! v
o
v
"#$
%&'
Fig 14.9, p. 436
Slide 13
v = speed of sound, vO = speed of observer
![Page 4: PHYSICS 231 INTRODUCTORY PHYSICS I](https://reader030.vdocuments.us/reader030/viewer/2022012708/61a88e52c546ea326e6fad3a/html5/thumbnails/4.jpg)
Doppler Effect:Source in Motion
! ' = ! " vsT
= ! " vs!
v
= ! 1" vs v( )
f ' = v! '
f ' = fv
v ! vs
!
" #
!
"
![Page 5: PHYSICS 231 INTRODUCTORY PHYSICS I](https://reader030.vdocuments.us/reader030/viewer/2022012708/61a88e52c546ea326e6fad3a/html5/thumbnails/5.jpg)
Doppler Effect, Source in Motion
Approaching source:
Source leaving:
f ' = fv
v ! vs
f ' = fv
v + vs
![Page 6: PHYSICS 231 INTRODUCTORY PHYSICS I](https://reader030.vdocuments.us/reader030/viewer/2022012708/61a88e52c546ea326e6fad3a/html5/thumbnails/6.jpg)
Example 14.6
An train has a brass band playing a song on a flatcar. Asthe train approaches the station at 21.4 m/s, a person onthe platform hears a trumpet play a note at 3520 Hz.DATA: vsound = 343 m/s
a) What is the true frequency of the trumpet?
b) What is the wavelength of the sound?
c) If the trumpet plays the same note after passing theplatform, what frequency would the person on theplatform hear?
a) 3300 Hz
b) 9.74 cm
c) 3106 Hz
![Page 7: PHYSICS 231 INTRODUCTORY PHYSICS I](https://reader030.vdocuments.us/reader030/viewer/2022012708/61a88e52c546ea326e6fad3a/html5/thumbnails/7.jpg)
Fig 14.11, p. 439
Slide 15
Shock Waves (Sonic Booms)
When the source velocity exceeds the speed of sound,
![Page 8: PHYSICS 231 INTRODUCTORY PHYSICS I](https://reader030.vdocuments.us/reader030/viewer/2022012708/61a88e52c546ea326e6fad3a/html5/thumbnails/8.jpg)
Application: speed radar
![Page 9: PHYSICS 231 INTRODUCTORY PHYSICS I](https://reader030.vdocuments.us/reader030/viewer/2022012708/61a88e52c546ea326e6fad3a/html5/thumbnails/9.jpg)
Application: weather radar
Both humidity (reflected intensity) and speed of clouds(doppler effect) are measured.
![Page 10: PHYSICS 231 INTRODUCTORY PHYSICS I](https://reader030.vdocuments.us/reader030/viewer/2022012708/61a88e52c546ea326e6fad3a/html5/thumbnails/10.jpg)
Doppler Effect:Both Observer and Source Moving
Switch appropriate signs if observeror source moves away
ƒ' = ƒv ± vo
v ± vs
!
"#$
%&
![Page 11: PHYSICS 231 INTRODUCTORY PHYSICS I](https://reader030.vdocuments.us/reader030/viewer/2022012708/61a88e52c546ea326e6fad3a/html5/thumbnails/11.jpg)
Example 14.7
At rest, a car’s horn sounds the note A (440 Hz). Thehorn is sounded while the car moves down thestreet. A bicyclist moving in the same direction at10 m/s hears a frequency of 415 Hz.DATA: vsound = 343 m/s.
What is the speed of the car? (Assume the cyclist isbehind the car)
31.3 m/s
![Page 12: PHYSICS 231 INTRODUCTORY PHYSICS I](https://reader030.vdocuments.us/reader030/viewer/2022012708/61a88e52c546ea326e6fad3a/html5/thumbnails/12.jpg)
Example 14.8a
A train has a whistle with a frequency of a 1000 Hz,as measured when both the train and observer arestationary. For a train moving in the positive xdirection, which observer hears the highest frequencywhen the train is at position x=0?
Observer A has velocity VA>0 and has position XA>0.Observer B has velocity VB>0 and has position XB<0.Observer C has velocity VC<0 and has position XC>0.Observer D has velocity VD<0 and has position XD<0.
![Page 13: PHYSICS 231 INTRODUCTORY PHYSICS I](https://reader030.vdocuments.us/reader030/viewer/2022012708/61a88e52c546ea326e6fad3a/html5/thumbnails/13.jpg)
Example 14.8b
A train has a whistle with a frequency of a 1000 Hz, asmeasured when both the train and observer arestationary. A train is moving in the positive xdirection. When the train is at position x=0,
An observer with V>0 and position X>0 hears afrequency:
a) > 1000 Hzb) < 1000 Hzc) Can not be determined
![Page 14: PHYSICS 231 INTRODUCTORY PHYSICS I](https://reader030.vdocuments.us/reader030/viewer/2022012708/61a88e52c546ea326e6fad3a/html5/thumbnails/14.jpg)
Example 14.8c
A train has a whistle with a frequency of a 1000 Hz,as measured when both the train and observer arestationary. A train is moving in the positive xdirection. When the train is at position x=0,
An observer with V>0 and position X<0 hears afrequency:
a) > 1000 Hzb) < 1000 Hzc) Can not be determined
![Page 15: PHYSICS 231 INTRODUCTORY PHYSICS I](https://reader030.vdocuments.us/reader030/viewer/2022012708/61a88e52c546ea326e6fad3a/html5/thumbnails/15.jpg)
Example 14.8d
A train has a whistle with a frequency of a 1000 Hz,as measured when both the train and observer arestationary. A train is moving in the positive xdirection. When the train is at position x=0,
An observer with V<0 and position X<0 hears afrequency:
a) > 1000 Hzb) < 1000 Hzc) Can not be determined
![Page 16: PHYSICS 231 INTRODUCTORY PHYSICS I](https://reader030.vdocuments.us/reader030/viewer/2022012708/61a88e52c546ea326e6fad3a/html5/thumbnails/16.jpg)
Standing Waves
Consider a wave and its reflection:
yright = Asin 2!x
"# ft
$%&
'()
*
+,
-
./
= A sin 2!x
"
$%&
'()cos2! ft # cos 2!
x
"
$%&
'()sin2! ft
012
345
yleft = Asin 2!x
"+ ft
$%&
'()
*
+,
-
./
= A sin 2!x
"
$%&
'()cos2! ft + cos 2!
x
"
$%&
'()sin2! ft
012
345
yright + yleft = 2Asin 2!x
"
$%&
'()cos2! ft
![Page 17: PHYSICS 231 INTRODUCTORY PHYSICS I](https://reader030.vdocuments.us/reader030/viewer/2022012708/61a88e52c546ea326e6fad3a/html5/thumbnails/17.jpg)
Standing Waves
•Factorizes into x-piece and t-piece •Always ZERO at x=0 or x=m!/2
yright + yleft = 2Asin 2!x
"
#$%
&'(cos2! ft
![Page 18: PHYSICS 231 INTRODUCTORY PHYSICS I](https://reader030.vdocuments.us/reader030/viewer/2022012708/61a88e52c546ea326e6fad3a/html5/thumbnails/18.jpg)
Resonances
Fig 14.16, p. 442
Slide 18
Integral number of halfwavelengths in length L
n!
2= L
![Page 19: PHYSICS 231 INTRODUCTORY PHYSICS I](https://reader030.vdocuments.us/reader030/viewer/2022012708/61a88e52c546ea326e6fad3a/html5/thumbnails/19.jpg)
Nodes and anti-nodes
• A node is a minimum in the pattern
• An antinode is a maximum
![Page 20: PHYSICS 231 INTRODUCTORY PHYSICS I](https://reader030.vdocuments.us/reader030/viewer/2022012708/61a88e52c546ea326e6fad3a/html5/thumbnails/20.jpg)
Fundamental, 2nd, 3rd... Harmonics
Fig 14.18, p. 443
Slide 25
Fundamental (n=1)
2nd harmonic
3rd harmonic
n!
2= L
![Page 21: PHYSICS 231 INTRODUCTORY PHYSICS I](https://reader030.vdocuments.us/reader030/viewer/2022012708/61a88e52c546ea326e6fad3a/html5/thumbnails/21.jpg)
Example 14.9
A cello string vibrates in its fundamental mode with afrequency of 220 vibrations/s. The vibrating segment is70.0 cm long and has a mass of 1.20 g.
a) Find the tension in the string
b) Determine the frequency of the string when itvibrates in three segments.
a) 163 N
b) 660 Hz
![Page 22: PHYSICS 231 INTRODUCTORY PHYSICS I](https://reader030.vdocuments.us/reader030/viewer/2022012708/61a88e52c546ea326e6fad3a/html5/thumbnails/22.jpg)
Beats
Interference from two waves with slightly differentfrequency
![Page 23: PHYSICS 231 INTRODUCTORY PHYSICS I](https://reader030.vdocuments.us/reader030/viewer/2022012708/61a88e52c546ea326e6fad3a/html5/thumbnails/23.jpg)
Beat Frequency Derivation
After time Tbeat, two sounds will differ by onecomplete cycle.
n1! n
2= 1
f1Tbeat ! f
2Tbeat = 1
Tbeat =1
f1! f
2
fbeat =1
Tbeatfbeat = f
1! f
2
![Page 24: PHYSICS 231 INTRODUCTORY PHYSICS I](https://reader030.vdocuments.us/reader030/viewer/2022012708/61a88e52c546ea326e6fad3a/html5/thumbnails/24.jpg)
Beats Demo
![Page 25: PHYSICS 231 INTRODUCTORY PHYSICS I](https://reader030.vdocuments.us/reader030/viewer/2022012708/61a88e52c546ea326e6fad3a/html5/thumbnails/25.jpg)
Standing waves in Pipes - Open both ends
Same expression for closed at both ends
!n= n
!
2
![Page 26: PHYSICS 231 INTRODUCTORY PHYSICS I](https://reader030.vdocuments.us/reader030/viewer/2022012708/61a88e52c546ea326e6fad3a/html5/thumbnails/26.jpg)
!n= (2n +1)
!
4
Standing waves in Pipes - Closed one end
![Page 27: PHYSICS 231 INTRODUCTORY PHYSICS I](https://reader030.vdocuments.us/reader030/viewer/2022012708/61a88e52c546ea326e6fad3a/html5/thumbnails/27.jpg)
Example 14.10
An organ pipe of length 1.5 m is open at one end.What are the lowest two harmonic frequencies?
DATA: Speed of sound = 343 m/s
57.2 Hz, 171.5 Hz
![Page 28: PHYSICS 231 INTRODUCTORY PHYSICS I](https://reader030.vdocuments.us/reader030/viewer/2022012708/61a88e52c546ea326e6fad3a/html5/thumbnails/28.jpg)
Example 14.11
An organ pipe (open at one end and closed at the other)is designed to have a fundamental frequency of 440 Hz.Assuming the speed of sound is 343 m/s,
a) What is the length of the pipe?
b) What is the frequency of the next harmonic?a) 19.5 cm
b) 1320 Hz
![Page 29: PHYSICS 231 INTRODUCTORY PHYSICS I](https://reader030.vdocuments.us/reader030/viewer/2022012708/61a88e52c546ea326e6fad3a/html5/thumbnails/29.jpg)
Interference of Sound Waves
Assume sources “a” and “b” are “coherent”. Ifobserver is located ra and rb from the two sources,
ra! r
b= n" formaximum
ra! r
b= (n +1 2)" forminimumra
rb
Source a Source b
Observer
![Page 30: PHYSICS 231 INTRODUCTORY PHYSICS I](https://reader030.vdocuments.us/reader030/viewer/2022012708/61a88e52c546ea326e6fad3a/html5/thumbnails/30.jpg)
Example 14.12
A pair of speakers separated by 1.75 m are driven by thesame oscillator at a frequency of 686 Hz. An observerstarts at one of the speakers and walks on a path that isperpendicular to the separation of the two speakers.(Assume vsound = 343 m/s)
a) What is the position of the last intensity maximum?
b) What is the position of the last intensity minimum?
c) What is the position of the first intensity maximum?
a) 2.81 m
b) 6.00 m
c) 27 cm