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solutions_39

# solutions_39 - PHY2061 R D Field Chapter 39 Solutions...

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PHY2061 R. D. Field Solutions Chapter 39 Page 1 of 10 Chapter 39 Solutions Problem 1: Observer A , on earth, signals with a flashlight every six minutes. Observer B is on a space station that is stationary with respect to earth. Observer C is on a rocket traveling from A to B with a constant speed of V = 0.6c relative to A. (a) At what intervals does B receive the signals from A (according to B )? (b) At what intervals does C receive the signals from A (according to A )? (c) At what intervals does C receive the signals from A (according to C )? Answer: (a) 6 min (b) 15 min (c) 12 min Solution: (a) Since A and B are at rest with respect to each other, B receives the pulses every six minutes (same as sent by A ). (b) Let 1 = first pulse leaves A , 2 = second pulse leaves A , etc.. Let a = first pulse reaches C , b = second pulse reaches C , etc.. Let the frame A be the rest frame of observer A and frame C be the rocket frame. Let t be the time between the first two pulses (in the A frame) and let t R be the time between the first two pulses received by C (as observed in the A frame) and t’ R be the time between the first two pulses received by C (as observed in the C frame). a Frame A x ct b 1 3 2 45 o Light Path Rocket Path c t c t R a Frame C x’ ct’ b 1 3 2 45 o Light Path c t R min 15 6 . 0 1 min 6 1 = = = + = β β t t t t c t c R R R min 12 25 . 1 min 15 ) ( = = = = + = γ γ γ R R R R R t t t c x t c t c B A C V

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PHY2061 R. D. Field Solutions Chapter 39 Page 2 of 10 Problem 2: A rocket travelling in the x direction at a constant speed of V = 0.7c emits radio waves at a rest frequency of 200 MHz to communicate with an observer A at rest on the x-axis as shown in the Figure . At what frequency ( in MHz ) should observer A tune his radio in order get a clear signal from the rocket, (a) when the rocket makes an angle θ = 135 o with the x-axis? (b) when the rocket makes an angle θ = 90 o with the x-axis? (c) when the rocket makes an angle θ = 45 o with the x-axis? Answer: (a) 282.9 (b) 142.9 (c) 95.6 Solution: We know that ) cos 1 ( 0 θ β γ + = f f with β = V/c = 0.7 and γ = 1.4 . Thus, (a) cos(135 o ) = -0.707 MHz MHz f f 9 . 282 ) 505 . 0 )( 4 . 1 ( 200 ) 707 . 0 1 ( 0 = = = β γ (b) cos(90 o ) = 0 MHz MHz f f 9 . 142 4 . 1 200 0 = = = γ (a) cos(45 o ) = 0.707 MHz MHz f f 6 . 95 ) 49 . 1 )( 4 . 1 ( 200 ) 707 . 0 1 ( 0 = = + = β γ A V x-axis θ
PHY2061 R. D. Field Solutions Chapter 39 Page 3 of 10 Problem 3: A point source of light is located 10 meters below the surface of a large lake ( n=1.3 ).

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