Physics 2101 Section 6 November 8 th : finish Ch.16

Transcription

1 Physics 2101 Section 6 November 8 th : finish Ch.16 Announcement: Exam # 3 (November 13 th ) Lockett 10 (6 7 pm) Nicholson 109, 119 (extra time 5:30 7:30 pm) Covers Chs Lecture Notes:

2 Transverse: Displacement of particle is perpendicular to the direction of wave propagation Transverse Traveling Wave 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 Wave Speed v wave = dx dt = ω k = λ T = λf y(x,0) = y max sin( kx) Spatially Periodic ( repeats ) : kλ = 2π Wave number k = 2π λ Wavelength v wave = τ µ = λf For transverse wave in physical medium

3 k = 2π λ ω = 2π T phase : kx ± ωt kx ωt kx + ωt Wave traveling in + x direction Wave traveling in - x direction

4

5 Interference Waves

6 Problem 16-33: Interference of Waves Two sinusoidal waves with the same amplitude y m =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 y 1 (x,t) = y m sin(kx ± ωt) Find (a) y m, (b) k, (c) ω, (d) φ 2, and the sign in front of ω. The two waves have the same λ and k They are in the same string so the velocity is the same v = ω k : so ω is same in both waves $ y'(x,t) = 2y m cos φ 2 % & 2 ' ( ) sin(kx + ± 1ωt ± 2 ωt 2 + φ 2 2 ) y' m = H 2 = 2y m cos φ 2 2 cos φ 2 2 = H 4y m v ± 1ω ± 1 ω = d 2k Δt need positive sign on both ω = dk Δt

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8 Standing Waves Define: Wavelength:

9 Standing Waves frequency wave velocity

10 Standing Waves

11 Example Solution: use T 1 + T 2 = 2T = Mg T 1 = T 2 = 1 2 Mg ν 1 = T 1 µ 1 = Mg 2µ 1 ν 2 = T 2 µ 2 = Mg 2µ 2

12 Example - con>nued use Solution: T 1 = M 1 g ν 1 = T 1 µ 1 = M 1g µ 1 T 2 = M 2 g ν 2 = T 2 µ 2 = M 2g µ 2

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

14 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 = τ µ = 150N 7.20x10 3 kg / m = m s (c) frequency f= v λ f = 144.3m / s 0.6m = 241Hz (b) Wavelengt λ: look at figure D = 3λ 2 : λ= 2 3 D = 0.60m

15 Problem 16-59

16 Solu>on for Problem From m = ρv = ρal ν 2 = τ µ 2 = τ ρ 2 A

17 Problem L 1 = L = n 1λ 1 2 = n 1 v 1 2 f L 2 = L = n 2λ 2 2 n 1 v 1 = n 2 v 2 = n 2v 2 2 f From ν 1 = τ 1 µ 1 = τ 1 µ ν 2 = τ 2 µ 2 = τ 2 µ n 1 n 2 = v 2 v 1 = τ 2 τ 1

18 frequency wave speed

19 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

20 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 Kelvin [K] Absolute zero and triple point of water 0 K K Conversion factors K C T C = T K (1 ΔK = 1 Δ C) C F T F = 9 5 T C + 32

21 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 T 1 = T 2 = T 3 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

22 18-4: Measuring Temperature Phase Diagram of Water Need two points and linear scale T=absolute zero Water triple point.

23 18-4: Measuring Temperature Triple Point of Water: Defined as T 3 = K The Constant-Volume Gas Thermometer 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. T of liquid defined at T=Cp p = p 0 + ρg( h)! p $ T = T 3 " # % & = (273.16K)! " # p 3 (C=constant) p p 3 $ % &

24 18-4: Measuring Temperature The Constant-Volume Gas Thermometer 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. T of liquid defined at T=Cp p = p 0 + ρg( h)! p $ T = T 3 " # % & = (273.16K)! p " # p 3 Still have a problem because answer depends upon p. p 3 $ % & " T = (273.16K) lim p 0 # $ p p 3 % & ' Keep V fixed: Figure shows Measurement for boiling water

25 18-4: Temperature Scales Checkpoint 1: The figure here shows three linear temperature scales with the freezing and boiling points of water indicated. (a) Rank the degrees on these scales by size, greatest first.

26 18-4: Temperature Scales Checkpoint 1: The figure here shows three linear temperature scales with the freezing and boiling points of water indicated. (b) Rank the following temperatures, highest first: 50 o X, 50 o W and 50 0 Y

27 Thermal expansion Most substances expand when heated and contract when cooled ZrW 2 O 8 is a ceramic with negative thermal expansion over a wide temperature range, K The change in length, ΔL ( = L - L 0 ), of almost all solids is ~ directly proportional to the change in temperature, ΔT ( = T - T 0 ) ΔL = αl 0 ΔT L = L 0 1+ αδt ( ) α = coefficient of thermal expansion What causes thermal expansion?

28 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? α steel = ( C) 1 ΔL = α steel L 0 ΔT = ( C) 1 (490m)(60 C) = 35 cm The solution is to use expansion joints

29 Thermal expansion and a Pendulum Clock T = 2π L g Problem 2: Pendulum Clock L = L 0 + ΔL = L 0 + α brass L 0 ΔT If the original period was 1 second # L 0 = 1s & % ( $ 2π ' 2 g = cm 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? ( ) L = cm 1+ ( / C)( 20 C) ( ) = cm = The new period is: T = 2π # ticks = 24 * 60*60 = # ticks = * = = s It runs slow (less time per tick) at 20 C at 0 C: fewer ticks = 1.7hr/yr

30 Example: Bimetal Strip Common device to measure and control temperature F = kx = kl 0 ( 1+ αδt )

31 18-6 Area Expansion Expansion in 1-D Expansion in 2-D ΔL = αl 0 ΔT ( ) L = L 0 1+ αδt A = L 0 ( 1+ αδt ) ( 1+ αδt ) #$ %& # $ W 0 %& ΔA = A 0 ( 1 + αδt ) 2 A 0 ( ) = A 0 2αΔT + ( αδt ) 2 A 0 ( 2α )ΔT A 0 βδt β = 2α

32 Thermal expansion of holes Do holes expand or contract when heated? Does radius increase or decrease when heated? The hole gets larger too!

33 Clicker Question 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

34 Volume expansion Expansion in 1-D Expansion in 3-D ΔL = αl 0 ΔT ( ) L = L 0 1+ αδt V = L 0 ( 1+ αδt) height width [ ][ W 0 ( 1+ αδt) ][ H 0 ( 1+ αδt) ] ΔV = V 0 ( 1+ αδt) 3 V 0 ( ( ) 2 + ( αδt) 3 ) = V 0 3αΔT + 3 αδt V 0 ( 3α)ΔT V 0 βδt β = coefficient of volume expansion Volume expansion coefficients solids : C liquids : C gasses : C 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 / C ]