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PHYIIHW1Solutions

# PHYIIHW1Solutions - hopkins(tlh982 HW01 criss(4908 This...

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hopkins (tlh982) – HW01 – criss – (4908) 1 This print-out should have 19 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 10.0 points At t = 0, a transverse wave pulse in a wire is described by the Function y = 5 e - x 2 / 2 , where x and t are given in SI units. Which Function describes this wave iF it is traveling in the negative x direction with a speed oF 4 . 5 m / s? 1. y = 5 e - ( x 2 - 4 . 5 t ) / 2 2. y = 5 e - x 2 / 2 + 4 . 5 t 3. y = 5 e - ( x - 4 . 5 t ) 2 / 2 4. y = 5 e - ( x 2 +4 . 5 t ) / 2 5. y = 5 e - x 2 / 2 - 4 . 5 t 6. y = 5 e - ( x +4 . 5 t ) 2 / 2 correct 7. y = 5 e - x 2 / 2 Explanation: ±or the wave traveling in the negative di- rection with the speed oF 4 . 5 m / s , we need to replace x with x + 4 . 5 t which gives y = 5 e - ( x +4 . 5 t ) 2 / 2 . 002 10.0 points A carbon steel piano wire 1 m long with a cross-sectional area oF 2 × 10 - 6 m 2 and mass 0 . 1 kg is stretched 30 mm. ±or carbon steel, the Young’s modulus is 2 × 10 11 N / m 2 . Determine the speed oF transverse waves on the string. Correct answer: 346 . 41 m / s. Explanation: Let : L = 1 m , Δ L = 30 mm , A = 2 × 10 - 6 m 2 , m = 0 . 1 kg , and Y = 2 × 10 11 N / m 2 . F = Y A Δ L L μ = m L v = r F μ = r Y A Δ L / L m / L = R Y A Δ L m = b (2 × 10 11 N / m 2 ) (2 × 10 - 6 m 2 ) 0 . 1 kg × (0 . 03 m) B 1 / 2 = 346 . 41 m / s . 003 (part 1 oF 4) 10.0 points A traveling wave propagates according to the expression y = (5 . 55 cm) sin[(1 . 98 cm - 1 ) x - (2 . 79 s - 1 ) t ] , where x is in centimeters, and t is in seconds. Determine the amplitude oF the wave. Correct answer: 5 . 55 cm. Explanation: Given a wave y = A sin( k x - ω t ), where the amplitude oF the wave is A . In our case, A = 5 . 55 cm . 004 (part 2 oF 4) 10.0 points Determine the wavelength oF the wave. Correct answer: 3 . 17333 cm. Explanation: The angular wave number oF the wave is k = 1 . 98 cm - 1 and its relation to the wavelength λ is λ = 2 π k = 3 . 17333 cm .

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hopkins (tlh982) – HW01 – criss – (4908) 2 005 (part 3 of 4) 10.0 points Determine the frequency of the wave. Correct answer: 0
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PHYIIHW1Solutions - hopkins(tlh982 HW01 criss(4908 This...

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