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hw03_sol

# hw03_sol - 3(a The time for the sound to travel from the...

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3. (a) The time for the sound to travel from the kicker to a spectator is given by d / v , where d is the distance and v is the speed of sound. The time for light to travel the same distance is given by d / c , where c is the speed of light. The delay between seeing and hearing the kick is Δ t = ( d / v ) – ( d / c ). The speed of light is so much greater than the speed of sound that the delay can be approximated by Δ t = d / v . This means d = v Δ t . The distance from the kicker to spectator A is d A = v Δ t A = (343 m/s)(0.23 s) = 79 m. (b) The distance from the kicker to spectator B is d B = v Δ t B = (343 m/s)(0.12 s) = 41 m. (c) Lines from the kicker to each spectator and from one spectator to the other form a right triangle with the line joining the spectators as the hypotenuse, so the distance between the spectators is ( ) ( ) 2 2 2 2 79m 41m 89m A B D d d = + = + = .

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13. (a) Consider a string of pulses returning to the stage. A pulse which came back just before the previous one has traveled an extra distance of 2 w , taking an extra amount of time Δ t = 2 w / v . The frequency of the pulse is therefore ( ) 2 1 343m/s 2.3 10 Hz. 2 2 0.75m v f t w = = = = × Δ (b) Since f 1/ w , the frequency would be higher if w were smaller.
16. Let the separation between the point and the two sources (labeled 1 and 2) be x 1 and x 2 , respectively. Then the phase difference is 1 2 1 2 1 2 2 ( ) 2 (4.40m 4.00m) 2 2 4.12rad.

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hw03_sol - 3(a The time for the sound to travel from the...

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