PHYSICS 231 INTRODUCTORY PHYSICS I
Transcript of PHYSICS 231 INTRODUCTORY PHYSICS I
PHYSICS 231
INTRODUCTORY PHYSICS I
Lecture 23
• 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
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
Doppler Effect:Source in Motion
! ' = ! " vsT
= ! " vs!
v
= ! 1" vs v( )
f ' = v! '
f ' = fv
v ! vs
!
" #
!
"
Doppler Effect, Source in Motion
Approaching source:
Source leaving:
f ' = fv
v ! vs
f ' = fv
v + vs
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
Fig 14.11, p. 439
Slide 15
Shock Waves (Sonic Booms)
When the source velocity exceeds the speed of sound,
Application: speed radar
Application: weather radar
Both humidity (reflected intensity) and speed of clouds(doppler effect) are measured.
Doppler Effect:Both Observer and Source Moving
Switch appropriate signs if observeror source moves away
ƒ' = ƒv ± vo
v ± vs
!
"#$
%&
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
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.
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
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
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
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
"
$%&
'()cos2! ft
Standing Waves
•Factorizes into x-piece and t-piece •Always ZERO at x=0 or x=m!/2
yright + yleft = 2Asin 2!x
"
#$%
&'(cos2! ft
Resonances
Fig 14.16, p. 442
Slide 18
Integral number of halfwavelengths in length L
n!
2= L
Nodes and anti-nodes
• A node is a minimum in the pattern
• An antinode is a maximum
Fundamental, 2nd, 3rd... Harmonics
Fig 14.18, p. 443
Slide 25
Fundamental (n=1)
2nd harmonic
3rd harmonic
n!
2= L
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
Beats
Interference from two waves with slightly differentfrequency
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
Beats Demo
Standing waves in Pipes - Open both ends
Same expression for closed at both ends
!n= n
!
2
!n= (2n +1)
!
4
Standing waves in Pipes - Closed one end
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
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
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
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