Waves, Temperature, and Other Physics Concepts (PDF)

Waves ! Wave is defined as a disturbance, oscillation or vibration that travels through space or matter that carry energy from point to another. ! Wave propagates through a medium (Solid, Liquid or Gas). ! Wave speed depends on the properties of the medium. ! Waves require a source and medium of...

Waves ! Wave is defined as a disturbance, oscillation or vibration that travels through space or matter that carry energy from point to another. ! Wave propagates through a medium (Solid, Liquid or Gas). ! Wave speed depends on the properties of the medium. ! Waves require a source and medium of propagation. ! Waves can be divided in to three categories: a) Mechanical waves: Water and Sound waves. b) Electromagnetic waves: light waves, X-ray waves, radio waves. c) Matter waves: Electrons photon and other fundamental particles waves. Types of Waves ! There are two types of waves a) Longitudinal waves: The particle displacement is parallel to the direction of wave propagation. Example (Sound waves or wave in a Strip) b) Transverse wave: The particle displacement is perpendicular to the direction of wave propagation. Example (wave in water or wave in a Strip) Wavelength and Frequency ! Wavelength and Frequency are a physical quantities used to describe waves. ! At a constant speed, wavelengths are inversely proportional to frequency. ! Wavelength measured in (meter)while frequency measured in (Hertz). ! The wave is expressed as a function of wavelength and frequency as Oscillation term ! y ( x, t ) = ASin ( kx − wt ) Phase term Speed of Travelling Waves ! The speed of travelling waves is given by v = λ f ! Whereas the wavenumber is expressed as 2π k= λ ! Example: ! A wave travelling along a string is described by y ( x, t ) = 0.00327 Sin ( 72.1x − 2.72t ) a) What is the amplitude of this wave? b) What are the wavelength, periodic time and frequency of this wave? c) What are the angular wavenumber and speed of this wave? Doppler Effect ! Doppler effect refers to the change in frequency of wave for a detector moving relative to the source. v ± vd fd = fs v ± vs The speed of Sound ! Sound is a longitudinal wave, alternating compressions and rarefactions in air or other medium. The speed of sound depends on the medium. sound wave passes through the air, the potential energy associated with compression and extensions of small volume element of the air, then the element of a medium changes in volume when pressure is changed. The speed of sound is given by B v= , ρ is the medium density. ρ β is the bulk modulus of the medium The speed of sound at 0˚C (273k) is 331m/s.The speed of sound at 20˚C (300k) is 343m/s. at room temperature. Doppler Effect ! Example: ! A person stands near a real station, he hears a train horn. The frequency of the horn is 500Hz, if the train is travelling at 20 m/s , what is the frequency he hears when the train is approaching?  343 ± 0  f d = 500    343 − 20  f d ≅ 531 Temperature Temperature The Zero law of thermodynamics Measuring Temperature The Celsius and Fahrenheit Fahrenheit and Kelvin Thermal expansion Temperature ! Temperature is a measurement of average kinetic energy of the molecules in the substances. ! The Zero Law of thermodynamics: ! The zero law, which has been called the logical afterthought, came to light only in the 1930. ! Zero Law came after first and second law of thermodynamics had been discovered and numbered. ! It is quite fundamental: the properties of many bodies change as change their temperature. For example, the volume of liquid increases as its temperature increased. The metal rod grows a little longer and electrical resistance increases as its temperature increased. The pressure of gas increased as the temperature increased. ! Zero law states that if bodies A and B are each in thermal equilibrium with a third body C, then they are in thermal equilibrium with each other. Temperature ! Measuring Temperature ! Liquid water, solid ice and water vapour (gaseous water) can coexist in thermal equilibrium at only one set of value of pressure and temperature. ! Gas-liquid and solid triple point at temperature and pressure for water is given by the international agreement T3 =273.16K=0.01˚C and P3=611.73Pa. ! At this point, it is possible to change all of the substance to ice, water or vapour by making small changes in pressure and temperature. Temperature ! The Celsius, Kalvin and Fahrenheit Scale ! The Kelvin scale used in basic Scientific work. ! The Celsius scale (formerly called the centigrade scale) is the scale of the choice for popular and commercial use and much scientific use. Celsius-Kelvin Scale C = K − 273.15o Celsius-Fahrenheit Scale 9 F = C + 32 5 Temperature ! Example: a. If the Fahrenheit temperature reading F=56F, what is the corresponding Celsius temperature reading? b. What is 100F in Celsius? c. What is 100F in Kelvin? Temperature Thermal Expansion Most metal expands when heated and contracted when cooled. Example, to preclude buckling therefore expansion slots are placed in bridge to accommodate railway expansion on hot days. Dental materials used for fillings must be matched in their thermal expansion properties otherwise consuming hot coffee or cold ice-cream would be quite painful. Temperature ! Linear Expansion ! If the temperature of a metal rod of length L is raised by an amount ΔT, its length is found to increase by an amount ΔL = LαΔT ! α is a constant called coefficient of linear expansion. ! α has the unit per degree or Kelvin. Temperature ! Volume Expansion ! If all dimensions of a solid expand with temperature, the volume of that solid must also expand. ! For liquid, volume expansion is the only meaningful expansion parameter. If the temperature of a solid or liquid whose volume V is increased by an amount ΔT the increase in volume is found to be V=Vβ∆T β is the coefficient of volume expansion of the solid or liquid, and β=3α Temperature For most common liquid, water does not behave like other liquids ! Above about 4˚C water expand as temperature increases, between 0˚C to 4˚C water contracts with increasing temperature. Temperature ! Example: ! On a hot day, an oil tracker loaded 37000L of diesel fuel. He encountered cold weather on the way, where the temperature was 23K, lower than before, and delivered his entire load. How many litres did he deliver? ! The coefficient of linear expansion for his steel truck tank is ! 11×10−6 o C and the coefficient of volume expansion for diesel fuel is 9.50 ×10−4 o C.  Temperature Heat Capacity Specific Heat Heat Transfer Mechanisms Temperature ! Heat Capacity the mount of heat required to raise the temperature of an object by 1˚C (without changing the state of matter). ! The heat capacity C of an object is the proportionality constant between the heat Q that the object absorbs or losses and the resulting temperature change of the object. Q = C ΔT = C (T f − Ti ) where ! T f and Ti is the final and initial temperature ! In the SI unit of heat capacity is J/˚K. Temperature ! Specific heat (c) is the amount of heat required to raise 1g of a material by 1˚C. Q = mcΔT Q = mc (T f − Ti ) ! The SI unit of specific heat (c) is (J/Kg.˚K). Temperature ! Example: ! What is the specific heat of aluminium if 2230 J are required to raise the temperature of a 45g sample from 30˚C to 85˚C? Q = cmΔT 2230 J c= = 901 0.045 × 55 Kg ⋅o K Temperature ! Example: How many kJ heat are required to raise the temperature of 365g of water from 68˚C to 90, given the specific heat of water is 4.180(J/g.˚c)? Q = cmΔT J o Q = 4.180 o × 365 g × 22 C g⋅ C Q = 33.57 kJ Temperature Example: When 600mL of water in an electrical kettle is heated from 20˚C to 85˚C to make a cup of tea, how much heat flows into water? Q = cmΔT m = ρV , ρ = 600ml = 0.6l = 0.6 ×10−3 m3 m = 1000 × 0.6 × 10−3 = 0.6kg. but J Q = 4.18 o × 0.6 ×103 g × 65 o C g⋅ C Q = 163000 J Q = 163kJ Temperature ! Heat Transfer Mechanisms ! There are three transfer mechanisms: a. Conduction, b. Convection, c. Radiation. Temperature Consider a slab of area A and thickness L a. Conduction: Q is the energy that transferred as heat through the slab from hot to cold reservoir, The conduction rate Pcond (the amount of energy transferred per unit time) Q T T Pcond = = KA H C T L K is the conduction constant depends on the material. Temperature b. Radiation Thermal radiation is expressed as Stefan-Boltzmann law Prad. = σε AT 4 σ = 5.6703 ×10−8 w m 2 , ε is the emissivity of the object's surface 0 < ε f from the mirror. 8  Mirror Equation Thus f and do are positive for concave mirrors. In the case of real images, di is positive. In cases where the image is virtual, di is negative. If the image is upright, then hi is positive and if the image is inverted, hi is negative. Using these sign conventions, we can express the mirror equation in terms of do, di, and the focal length f: 1 1 1 + = do di f The magnification m of the mirror is defined to be: di hi m=− = do ho 9 Problem : Where do you have to place an object in front of a concave mirror with focal length f if the image is to be of the same size as the object ? di hi m =− = =1 A) do=0.5f do ho B) do=f di = do C) do=2f 1 1 1 2 + = = do do f do do = 2 f 10 Images from Convex Mirrors In the case of a convex mirror, we define the focal length f to be negative because the focal point of the mirror is on the opposite side of the object. We always take the object distance do to be positive. We recall the mirror equation: 1 1 1 + = do di f We can rearrange the mirror equation to get: do f di = do − f If do is always positive and f is always negative, we can see that di will always be negative. 11 Problem: A concave spherical mirror has a radius of 10 cm. Calculate a) The focal length. b) The location of the image from a mirror when object a distance 15 cm from the mirror. c) The magnification of a mirror. d) The image size if the size of object about 8mm Answer: a) R 10 c) -di -7.5 f = = = 5cm m = = = -0.5 2 2 d0 15 1 1 1 + = d0 di f hi hi d) m= = = 0.5 b) 1 + 1 = 1 h0 8 15 di 5 1 = 1 - 1 = 2 hi = 8 x0.5 = 4 mm di 5 15 15 15 di = = 7.5cm 2 12 Problem : A small object is placed in front of a converging mirror with radius R = 7.50 cm such that the image distance equals the object distance. How far is this small object from the mirror? 1 1 1 1 1 2 A. 2.50 cm + = = + = do di f d d d B. 5.00 cm C. 7.50 cm d=2f D. 10.0 cm R f= E. 15.0 cm 2 ⎛ R ⎞⎟ d = 2⎜⎜ ⎟⎟ = R = 7.50 cm ⎜⎝ 2 ⎟⎠ 13  Example: A concave spherical mirror has a radius of 10 cm. Calculate the location and size of an 8mm object a distance 2.5 cm from the mirror. 1 1 2 1 + = = d 0 di R f d i = -5cm -di m= = 2.0 d0 y = 8 mm Example: A convex sideview mirror has a radius of curvature of 12.0 m and that a car is 9.0 m behind the mirror. Find the image distance and the magnification for this convex mirror. R = - 12 cm since it is convex mirror, d0 = 9 m f =R / 2 = -12 / 2 = - 6 cm 1 1 1 + = d 0 di f 1 1 1 + = 9 di -6 1 1 1 -4 =- - = di 6 9 18 -18 di = = -4.5m 4 14 Example: We place an object with height ho = 5.00 cm at a distance do = 16.0 cm from a thin converging lens with focal length f = 4.00 cm What is the image distance? What is the linear magnification of the image? What is the image height? 5.33 cm. , m = (-di/do) = – 0.333 , hi = mho = –1.67 cm The image height is negative, so the image is inverted, as we expected from the negative magnification 15  Refraction and Snell’s Law When the light passes between two different transparent medium, it will be refracted. The speed of light is different in different media. The refractive index (n) of a medium is a ratio of speed of light in space (c) to the speed of light in the medium (v) n = (c/v) The Snell's law n1 sin θ1 = n2 sin θ2 16 Example: What is the speed of light in crown glass, whose index of refraction is 1.52? Example: A light ray is incident from water, whose index of refraction is 1.33, on a plate of glass whose index of refraction is 1.73. What angle of incidence will result if the refraction angle is 200. Example: A light ray is incident from air (n =1), with an incident angle of 300 on different material. Find the refractive index of material and speed of light in it if the refraction angle 200. 17  The power of the lens The inverse of the focal length is called the lens power, P, P = 1/ f The power of the lens is measured in diopters, D, with 1 D = 1 m–1. Eyeglasses and contact lenses are typically characterized in terms of their diopter value. October 21, 2024 18  Problems 1- A light incident on a planar mirror with the incident angle of 25, then the reflected angle is According to the law of reflection, the angle of reflection equals the angle of incidence. So the angle of reflection (measured to the normal) is also 25o. 2- A person sits 2.0 m in front of a plane mirror. What is the location of the image from a mirror in m. In-plane mirror, the image is formed behind the mirror at the same distance as the object is kept in front of the mirror. Therefore, if an object of 2 m is placed in front of a plane mirror, then its image formed is virtual, erect, and 2 m behind the mirror 3-A person sits 1.5 m in front of a plane mirror. What is the location of the image from him? In the plane mirror, the image distance is always equal to the object distance from the mirror. According to the question, the object distance is 1.5 m so the image distance will be 1.5 m and the distance between the object and image will be 3 m. 4-Light is incident on a flat surface, making an angle of 70o with that surface, as shown in the figure. (a) What is the angle of incidence? (b) What is the angle of reflection? a) If the light makes an angle of 70o with the surface, it makes an angle of 200 with the normal to the surface. Thus the angle of incidence is: 90o – 70o = 20o b) According to the law of reflection, the angle of reflection equals the angle of incidence. So the angle of reflection (measured to the normal) is also 20o. 19 -A beam of light reflects and refracts at point A on the interface between material 1 with index of refraction 𝑛1 = 1.33 and material 2 with index of refraction 𝑛2 = 1.77. The incident beam makes an angle of 50∘ with the interface (surface). a) What is the angle of reflection at point A? b) What is the angle of refraction there? a) The angle of incidence is 90 − 50 = 40° From the law of reflection: Thus: angle of reflection = 40° b) From Snell’s law 𝑠𝑖𝑛𝜃2 = 𝑛1/ 𝑛2 𝑠𝑖𝑛 𝜃 1 𝑠𝑖𝑛𝜃2 = 1.33/1.77 𝑠𝑖𝑛 40 = 0.483 𝜃2 = sin−1 0.483 = 28.88° 6- Light in vacuum is incident on the surface of a glass slab. In vacuum the beam makes an angle of 32.0∘ with the normal to the surface, while in the glass it makes an angle of 21.0∘ with the normal. What is the index of refraction of the glass? Solution: 𝑛1 = 1 𝜃1=32° 𝜃2 = 21° 𝑛2 = ? 𝑛 1sin𝜃1 =𝑛2 sin𝜃2 𝑛2 = 𝑛 1sin𝜃1 / sin𝜃2 =sin 32/sin 21= 1.48 20