physics 2101 section 6 november 8 finish ch

Physics 2101 Section 6

November 8th: finish Ch.16

Lecture Notes: http://www.phys.lsu.edu/classes/fall2012/phys2101-6/

Announcement: •  Exam # 3 (November 13th) Lockett 10 (6 – 7 pm) Nicholson 109, 119 (extra

time 5:30 – 7:30 pm) Covers Chs. 11.7-15

Transverse Traveling Wave

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y(x,0) = ymax sin kx( )

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k =2πλ

Spatially Periodic ( repeats ) : kλ = 2π

Wave number Wavelength

Transverse: Displacement of particle is perpendicular to the direction of wave propagation

Longitudinal: Displacement (vibration) of particles

is along same direction as motion of wave

Traveling Waves - they travel from one point to another Standing Waves - they look like they’re standing still

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vwave =dxdt

=ωk

=λT

= λf

Wave Speed

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vwave =τµ

= λf For transverse wave in physical medium

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k =2πλ

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ω =2πT

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phase : kx ±ωt

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kx +ωt⇒

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kx −ωt⇒ Wave traveling in + x direction

Wave traveling in - x direction

Interference  Waves  

Problem  16-­‐33:  Interference  of  Waves  Two sinusoidal waves with the same amplitude ym=9.00 mm and the same wavelength λ travel together along a string that is stretched along the x axis. Their resultant wave is shown twice in the figure, as the valley A travels in the negative direction by a distance d=56.0 cm in Δt=8.0 ms. The tick marks along the x axis are separated by Δx=10 cm, and the height H is 8.0mm. Assume the first wave is given by Find (a) y’m, (b) k, (c) ω, (d) φ2, and the sign in front of ω.

y1(x,t) = ym sin(kx ±ωt)

The two waves have the same λ and kThey are in the same string so the velocity is the same

v =ωk

: so ω is same in both waves

y '(x,t) = 2ym cosφ2

2$

%&'

()sin(kx + ±1ωt ±2 ωt

2+φ2

2)

y 'm =H2= 2ym cos

φ22

cosφ22=

H4ymv ≡ ±1ω ±1 ω

2k=dΔt

need positive sign on both

ω =dkΔt

Standing  Waves  

Wavelength: Define:

Standing  Waves  

frequency

wave velocity

       Standing  Waves  

Example  

Solution: use

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T1 +T2 = 2T = Mg

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T1 = T2 =12Mg

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ν2 =T2µ2

=Mg2µ2

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ν1 =T1µ1

=Mg2µ1

Example  -­‐  con>nued  

Solution:

use

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T1 = M1g

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T2 = M2g

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ν2 =T2µ2

=M2gµ2

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ν1 =T1µ1

=M1gµ1

Problem  16-­‐58  

b) If the mass of the block is m, what is the corresponding n?

Problem  16-­‐49:  Standing  waves/resonances  

A nylon guitar string has a linear density of µ=7.20 g/m and is under a tension of τ=150 N. The fixed supports are a distance D=90. cm apart. It oscillates with the pattern shown in the figure. Calculate the (a) speed, (b) wavelength, and (c) frequency of wave.

(a) Speed of wave

v =τµ=

150N7.20x10−3kg / m

= 144.3ms

(b) Wavelengt λ: look at figure

D =3λ2

: λ= 23D = 0.60m

(c) frequency f= vλ

f =144.3m / s

0.6m= 241Hz

Problem  16-­‐59  

Solu>on  for  Problem  16-­‐59  

From

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m = ρV = ρAL

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ν2 =τµ2

=τρ2A

Problem  16-­‐11  

From

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ν 2 =τ 2µ2

=τ 2µ

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ν1 =τ1µ1

=τ1µ

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L1 = L =n1λ12

=n1v12 f

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L2 = L =n2λ22

=n2v22 f

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n1v1 = n2v2

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n1n2

=v2v1

=τ 2τ1

frequency

wave speed

Chapter  18:  Temperature,  Heat,  and  Thermodynamics    

Definitions

“System”- particular object or set of objects

“Environment” - everything else in the universe

What is “State” (or condition) of system?

- macroscopic description - in terms of detectable quantities:

volume, pressure, mass, temperature (“State Variables”)

Study of thermal energy --> temperature

Temperature  &  Thermometers  

Linear scale : need 2 points to define

Fahrenheit [° F] body temp and ~1/3 of body temp ~100 ° F ~33 ° F Celsius [° C] “freezing point” and “boiling point” of water 0 ° C 100 ° C

Conversion factors K→ ° C ° C → ° F

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TF = 95TC + 32

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TC =TK − 273.15 (1 ΔK = 1 ΔC)

Kelvin [K] Absolute zero and triple point of water 0 K 273.16 K

18-­‐3:  Zeroth  Law  of  Thermodynamics    

Defines THERMAL EQUILIBRIUM If two systems are in thermal equilibrium with a third, then they are in

thermal equilibrium with each other T1 = T2 = T3

No Heat flow

In this case: a)  A is in thermal equilibrium with T

b) B is in thermal equilibrium with T

c) A & B are in thermal equilibrium

18-­‐4:  Measuring  Temperature  

Phase Diagram of Water

Need two points and linear scale T=absolute zero

Water triple point.

18-­‐4:  Measuring  Temperature  

Triple Point of Water: Defined as T3=273.16 K

A gas filled bulb is connected to a Hg manometer. The pressure volume can be maintained constant by raising or lowering the the Hg level in reservoir R.

The Constant-Volume Gas Thermometer

T of liquid defined at T=Cpp = p0 + ρg(−h)

T = T3pp3

!

"#$

%&= (273.16K ) p

p3

!

"#$

%&

(C=constant)

18-­‐4:  Measuring  Temperature  

A gas filled bulb is connected to a Hg manometer. The pressure volume can be maintained constant by raising or lowering the the Hg level in reservoir R.

The Constant-Volume Gas Thermometer

T of liquid defined at T=Cpp = p0 + ρg(−h)

T = T3pp3

!

"#$

%&= (273.16K ) p

p3

!

"#$

%&

Still have a problem because answer depends upon p.

T = (273.16K ) lim p→0pp3

"

#$%

&'

Keep V fixed: Figure shows Measurement for boiling water

Checkpoint  1:    The  figure  here  shows  three  linear  temperature  scales  with  the  freezing  and  boiling  points  of  water  indicated.        

18-­‐4:  Temperature  Scales  

(a) Rank the degrees on these scales by size, greatest first.

Checkpoint  1:    The  figure  here  shows  three  linear  temperature  scales  with  the  freezing  and  boiling  points  of  water  indicated.        

18-­‐4:  Temperature  Scales  

(b) Rank the following temperatures, highest first: 50oX, 50o W and 500 Y

Thermal  expansion  Most substances expand when heated

and contract when cooled

ZrW2O8 is a ceramic with negative thermal expansion over a wide temperature range, 0-1050 K

The change in length, ΔL ( = L - L0 ), of almost all solids is ~ directly proportional to the change in temperature, ΔT ( = T - T0 )

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ΔL =αL0ΔTL = L0 1+αΔT( )

α = coefficient of thermal expansion

What causes thermal expansion?

Thermal  expansion  of  the  Brooklyn  Bridge  

Problem 1: Brooklyn Bridge Expansion The steel bed of the main suspension bridge is 490 m long at + 20°C. If the extremes in temperature are - 20°C to + 40°C, how much will it contract and expand?

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α steel =12 ×10−6(°C)–1

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ΔL =α steelL0ΔT=12 ×10−6(°C)–1(490m)(60°C)= 35 cm

The solution is to use expansion joints

Thermal  expansion  and  a  Pendulum  Clock  

A pendulum clock made of brass is designed to keep accurate time at 20°C. If the clock operates at 0°C, does it run fast or slow? If so, how much?

Problem 2: Pendulum Clock

If the original period was 1 second

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T = 2π Lg

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L = L0 + ΔL= L0 +αbrassL0ΔT

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L0 =1s2π#

$ %

&

' ( 2

g = 24.824 cm

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L = 24.824 cm 1+ (19 ×10−6 /°C)(−20°C)( )= 24.824 cm 0.9996( )= 24.814

The new period is:

T = 2π 24.8149.8

= 0.9998 s

It runs slow (less time per tick) at 20°C at 0°C: fewer ticks = 1.7hr/yr

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# ticks = 24 *60*60 = 86400# ticks = 86400 *0.999 = 86383

Example:  Bimetal  Strip      

Common device to measure and control temperature

F = kx = kL0 1+αΔT( )

18-­‐6  Area  Expansion    

Expansion in 1-D

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ΔL =αL0ΔTL = L0 1+αΔT( )

A = L0 1+αΔT( )#$ %& W0 1+αΔT( )#$ %&Expansion in 2-D

ΔA = A0 1+αΔT( )2 − A0= A0 2αΔT + αΔT( )2( )≅ A0 2α( )ΔT≅ A0βΔT

β = 2α

Thermal  expansion  of  holes  

Do holes expand or contract when heated?

Does radius increase or decrease

when heated?

The hole gets larger too!

When  the  temperature  of  the  piece  of  metal  shown  below  is  increased  and  the  expands    metal  expands,  what  happens  to  the  gap  between  the  ends?    

1.  It  becomes  narrower  2.  It  becomes  wider  3.  It  remains  unchanged  

Clicker Question

Volume  expansion  

Expansion in 1-D

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ΔL =αL0ΔTL = L0 1+αΔT( )

width

heig

ht

Expansion in 3-D

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V = L0 1+αΔT( )[ ] W0 1+αΔT( )[ ] H 0 1+αΔT( )[ ]

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ΔV =V0 1+αΔT( )3 −V0=V0 3αΔT + 3 αΔT( )2 + αΔT( )3( )

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≅V0 3α( )ΔT≅V0βΔT β = coefficient of volume expansion

Problem 3: Gas tank in the sun The 70-L steel gas tank of a car is filled to the top with gasoline at 20°C. The car is then left to sit in the sun, and the tank reaches a temperature of 40°C. How much gasoline do you expect to overflow from the tank? [gasoline has a coefficient of volume expansion of 950×10-6/°C ]

Volume expansion coefficients

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solids : 1− 87 ×10−6 C liquids : 210 −1100 ×10−6 C gasses : 3400 ×10−6 C