# beats - Sheet1 BEATS t= f1 = f2 = f2 - f1 = A1 = A2 =...

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Sheet1 Page 1 BEATS 0 s 400 Hz 2513.27 rad/s 0 s 430 Hz 2701.77 rad/s 0 s 30 Hz 1 1 t (s) 0 1 1 2 0 0.93 0.92 1.85 0 0.73 0.69 1.42 0 0.43 0.35 0.77 0 0.06 -0.05 0.01 0 -0.31 -0.44 -0.75 0 -0.64 -0.76 -1.4 0 -0.88 -0.95 -1.83 0 -0.99 -0.99 -1.99 0 -0.97 -0.87 -1.84 0 -0.81 -0.61 -1.42 0 -0.54 -0.25 -0.79 0 -0.19 0.15 -0.04 0 0.19 0.53 0.72 0 0.54 0.82 1.36 0 0.81 0.98 1.79 0 0.97 0.98 1.95 0 0.99 0.82 1.81 0 0.88 0.53 1.41 0 0.64 0.15 0.79 0 0.31 -0.25 0.06 0 -0.06 -0.61 -0.67 0 -0.43 -0.87 -1.3 0 -0.73 -0.99 -1.72 0 -0.93 -0.95 -1.88 0 -1 -0.76 -1.76 0 -0.93 -0.44 -1.37 0 -0.73 -0.05 -0.78 0 -0.43 0.34 -0.08 0 -0.06 0.69 0.62 0 0.31 0.92 1.23 0 0.64 1 1.64 0 0.88 0.92 1.8 0 0.99 0.69 1.68 0.01 0.97 0.35 1.32 0.01 0.81 -0.05 0.76 0.01 0.54 -0.44 0.1 0.01 0.19 -0.76 -0.57 0.01 -0.19 -0.95 -1.14 0.01 -0.54 -1 -1.53 0.01 -0.81 -0.88 -1.69 t = f 1 = ϖ 1 = T 1 = f 2 = ϖ 2 = T 2 = f 2 - f 1 = A 1 = x 1 = A 1 cos ϖ 1 t A 2 = x 2 = A 2 cos ϖ 2 t x 1 x 2 x 1 + x 2 0 0.01 0.02 0.03 0.0 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 Beats time x1 + x2 0 0.01 0.02 0.03 0.0 -1.5 -1 -0.5 0 0.5 1 1.5 Compone time amplitude

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Sheet1 Page 2 0.01 -0.97 -0.62 -1.58 0.01 -0.99 -0.25 -1.25 0.01 -0.88 0.15 -0.73 0.01 -0.64 0.53 -0.11 0.01 -0.31 0.82 0.51 0.01 0.06 0.98 1.04 0.01 0.43 0.98 1.41 0.01 0.73 0.82 1.55 0.01 0.93 0.53 1.46 0.01 1 0.16 1.16 0.01 0.93 -0.25 0.68 0.01 0.73 -0.61 0.12 0.01 0.43 -0.87 -0.45 0.01 0.06 -0.99 -0.93 0.01 -0.31 -0.96 -1.26 0.01 -0.64 -0.76 -1.4 0.01 -0.88 -0.45 -1.32 0.01 -0.99 -0.06 -1.05 0.01 -0.97 0.34 -0.63 0.01 -0.81 0.68 -0.12 0.01 -0.54 0.92 0.38 0.01 -0.19 1 0.81 0.01 0.19 0.92 1.11 0.01 0.54 0.69 1.23 0.01 0.81 0.35 1.16 0.01 0.97 -0.04 0.92 0.01 0.99 -0.43 0.56 0.01 0.88 -0.75 0.12 0.01 0.64 -0.95 -0.31 0.01 0.31 -1 -0.69 0.01 -0.06 -0.88 -0.94 0.01 -0.43 -0.62 -1.04 0.01 -0.73 -0.26 -0.99 0.01 -0.93 0.14 -0.79 0.01 -1 0.52 -0.48 0.01 -0.93 0.82 -0.11 0.01 -0.73 0.98 0.25 0.01 -0.43 0.98 0.56 0.01 -0.06 0.83 0.76 0.01 0.31 0.54 0.84 0.01 0.64 0.16 0.8 0.01 0.88 -0.24 0.63 0.01 0.99 -0.61 0.39 0.01 0.97 -0.87 0.1 0.01 0.81 -0.99 -0.18 0.01 0.54 -0.96 -0.42 0.01 0.19 -0.76 -0.58 0.01 -0.19 -0.45 -0.64 0.01 -0.54 -0.06 -0.6 0.01 -0.81 0.34 -0.47 0.01 -0.97 0.68 -0.29 0.01 -0.99 0.92 -0.08 0.01 -0.88 1 0.12
Sheet1 Page 3 0.01 -0.64 0.92 0.29 0.01 -0.31 0.7 0.39 0.01 0.06 0.36 0.42 0.01 0.43 -0.04 0.38 0.01 0.73 -0.43 0.3 0.01 0.93 -0.75 0.18 0.02 1 -0.95 0.05 0.02 0.93 -1 -0.07 0.02 0.73 -0.88 -0.15 0.02 0.43 -0.62 -0.19 0.02 0.06 -0.26 -0.2 0.02 -0.31 0.14 -0.17 0.02 -0.64 0.52 -0.12 0.02 -0.88 0.81 -0.06 0.02 -0.99 0.98 -0.01 0.02 -0.97 0.98 0.01 0.02 -0.81 0.83 0.02 0.02 -0.54 0.54 0 0.02 -0.19 0.16 -0.02 0.02 0.19 -0.24 -0.05 0.02 0.54 -0.6 -0.07 0.02

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## This note was uploaded on 04/17/2008 for the course PHYSICS 1200 taught by Professor Peterpersans during the Spring '08 term at Rensselaer Polytechnic Institute.

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beats - Sheet1 BEATS t= f1 = f2 = f2 - f1 = A1 = A2 =...

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