課程名稱︰普通物理學甲上 課程性質︰必修 課程教師︰張寶棣 開課學院：理學院 開課系所︰物理學系 考試日期（年月日）︰101/1/12 考試時限（分鐘）：120mins(大約) 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 1.Please answer the following questions.(15%) (a)Describe the twin paradox and explain why it does not lead to a controversial result. (b)List at least three differences between particles and waves. (c)The most exciting white water for canoeing often occurs when the river narrows. Why? 2.Transverse Doppler Effect. The Doppler effect may happen when the source of light and detector approach one another at an angle θ as shown in Fig. 1. If the source emits light with frequency f in the source rest frame, what is the frequency detected by the detector at the angle θ? Discuss the case when θ=90度. (10%)(Hint: in relativistic Doppler effect, you need to consider both source moving the time dilation.) v Source →......................... . . . . . . . . . . .r .R . . . . . . . . . . . . Figure 1: θ .O 3.Stellar Aberration. Imagine that Earth were at rest with respect to a distant star and that an Earthbound telescope had to be pointed at angle θ above the horizon to view the star. Now suppose that there is a relative velocity v between Earth and the star. The angle θ would change to θ'. (a)Express cosθ' in terms of cosθ,v and c. (b)If v/c is small, show that cosθ'≒cosθ+(v/c)sin^2(θ).(10%) This effect is called stellar aberration and is significant in astronomical observation. It is particular important when we compare the position of a star in the sky in winter to its position in summer, because the velocity of Earth reverse relative to the star every 6 months. (Hint: Let Earth be at the origin and the star be somewhere in the first quadrant. Now the star is moving away from Earth with velocity v in x.) 4.A couple of astronauts took a spacecraft to a certain galaxy. When they left the Earth with a constant speed of 0.95c, the female astronaut found that she was pregnant. After 10 months spacecraft time, a male baby was born and the male astronaut immediately sent out the message to the Earth with speed of light to apply for a birth certificate. If we neglect the acceleration time that the spacecraft took off, how far was the spacecraft oberved by the Earth people when the baby was born? When did the application signal reach the Earth according to the city goverment? If the date that the couple left is March 2nd, 2040, what is the birthday of the baby in the Earth time?(15%) 5.A standing wave pattern on a string is described by y(x,t)=0.04sin(5πx)cos(40πt), where x and y are in meters and t is in seconds. (a)Determine the locations of all nodes for 0.00≦x≦0.40m.(4%) (b)What is the period of the oscillatory motion of any (nonode) point on the string.(4%) (c)What are the speed and the amplitude of the two traveling waves that intergere to produce this wave?(8%) (d)At what times for 0.000≦t≦0.050s will all the points on the string have zero transverse velocity?(4%) 6.Hovering over the pit of hell, the devil observes that as a student falls past (within terminal velocity), the frequency of his scream decreases from 842 to 820 Hz. (a)Find the speed of descent of the student. (b)The student's scream reflects from the bottom of the pit. Find the frequency of the echo as heard by the student. (c)Find the frequency of the echo as heard by the devil. Assum that the speed of sound is 343 m/s.(10%) 7.A siphon is a device for removing liquid from a container. It operates as shown in Fig.2. Tube ABC must initially be filled, but once this has been done, liquid will flow through the tube until the liquid surface in container is level with the tube opening at A. The liquid has density ρ and negligible viscosity. (a)With what speed does the liquid emerge from the tube at C? (b)What is the pressure in the liquid at the topmost point B? (c)Theoretically what is the greatest possible h_1 that a siphon can lift water?(15%) ..B -- .. .. ↑ . . . . h_1 | . | . | . | . ↓ |-----------.---| . -- | . | . ↑ | . | . | . | . d | . | . | . | . ↓ | .A | . -- | | . ↑ | | . | | . h_2 |---------------| . . ↓ .C -- Figure 2( . 表充滿水水管) 8.Show how it is possible for one who knows the A- and B-coordiate intervals between two events to construct the correspinding Lorentz diagram and from it find geometrically the relative speed between the A- and B-frames.(5%) --

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