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wave_problems - 1 Problems 15.27 15.37 15.41 15.79(1...

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1 Problems . 15 . 27 , 15 . 37 , 15 . 41 , 15 . 79 (1) 1. ( Estimates ) Estimate the mass per length of a double bass string. The lowest note on the bass is an E 1, ringing in at a cool 41 Hz just above human hearing. Based on the picture below, estimate the wavelength of this fundamental mode, and the velocity of a wave in the double bass string. Estimate the tension in the double bass low E string – give your answer in pounds and newtons. 2. ( Sinusoidal averages ) We have argued that sin 2 ( kx - ωt ) = 1 2 using the fact that sin 2 + cos 2 = 1. Here we would like to show result this more directly. The average of sin 2 and cos 2 over a period T is sin 2 2 πt T 1 T Z T 0 d t sin 2 2 πt T (2) cos 2 2 πt T 1 T Z T 0 d t cos 2 2 πt T (3) These integrals are computed by using the identity sin 2 ( x ) = 1 2 - 1 2 cos(2 x ) (4) cos 2 ( x ) = 1 2 + 1 2 cos(2 x ) (5) (a) Draw a graph of sin 2 ( x ) and cos 2 ( x ) and give a graphical explanation of the indentities given in Eq. 4 and Eq. 5. (b) Use these triginometic identities given to perform the integrals in Eq. 2 and Eq. 3 and show the result sin 2 = cos 2 = 1 2 3. ( Power )
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