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Chapter 17 Solutions_8_1

Chapter 17 Solutions_8_1 - Chapter17 3(a)/v,wheredisthe...

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Chapter 17 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 = + = + = . 10. (a) The amplitude of a sinusoidal wave is the numerical coefficient of the sine (or cosine) function: p m = 1.50 Pa. (b) We identify k = 0.9 π and ω = 315 π (in SI units), which leads to f = ω /2 π = 158 Hz. (c) We also obtain λ = 2 π / k = 2.22 m. (d) The speed of the wave is v = ω / k = 350 m/s.
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