# HW12 - homework 12 – GAUTHIER JOSEPH – Due 1:00 am 1...

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Unformatted text preview: homework 12 – GAUTHIER, JOSEPH – Due: Nov 21 2007, 1:00 am 1 Question 1, chap 16, sect 2. part 1 of 1 10 points What is the frequency corresponding to a period of 0 . 81 s? Correct answer: 1 . 23457 Hz (tolerance ± 1 %). Explanation: Let : t = 0 . 81 s . f = 1 t = 1 . 81 s = 1 . 23457 Hz . Question 2, chap 16, sect 2. part 1 of 1 10 points A harmonic wave is traveling along a rope. The oscillator that generates the wave com- pletes 42.0 vibrations in 23.9 s. A given crest of the wave travels 424 cm along the rope in a time period of 12.3 s. What is the wavelength? Correct answer: 0 . 19616 m (tolerance ± 1 %). Explanation: Basic Concepts: v = f λ f = number of vibrations t Δ x = v Δ t Given: n = 42 . 0 vibrations t = 23 . 9 s Δ x = 424 cm Δ t = 12 . 3 s Solution: λ = v f = Δ x Δ t n t = Δ xt n Δ t = (424 cm)(23 . 9 s) 42 (12 . 3 s) · 1 m 100 cm = 0 . 19616 m Question 3, chap 16, sect 2. part 1 of 2 10 points Tension is maintained in a string as in the figure. The observed wave speed is 20 m / s when the suspended mass is 3 . 3 kg . The acceleration of gravity is 9 . 8 m / s 2 . 3 . 3 kg What is the mass per unit length of the string? Correct answer: 0 . 08085 kg / m (tolerance ± 1 %). Explanation: Let : v = 20 m / s and m = 3 . 3 kg . The tension in the string is F = mg and its velocity is v = radicalBigg F μ , and μ = F v 2 = mg v 2 = (3 . 3 kg) ( 9 . 8 m / s 2 ) (20 m / s) 2 = . 08085 kg / m . homework 12 – GAUTHIER, JOSEPH – Due: Nov 21 2007, 1:00 am 2 Question 4, chap 16, sect 2. part 2 of 2 10 points What is the wave speed when the suspended mass is 1 . 8 kg? Correct answer: 14 . 771 m / s (tolerance ± 1 %). Explanation: Let : m = 1 . 8 kg . The velocity is v = radicalBigg F μ = radicalbigg mg μ = radicalBigg (1 . 8 kg) (9 . 8 m / s 2 ) . 08085 kg / m = 14 . 771 m / s . Question 5, chap 16, sect 2. part 1 of 1 10 points A light string of mass 15 . 9 g and length 3 . 03 m has its ends tied to two walls that are separated by the distance 2 . 34 m. Two objects, each of mass 1 . 4 kg, are suspended from the string as in the figure. The acceleration of gravity is 9 . 8 m / s 2 . 1 . 4 kg 1 . 4 kg . 7 5 7 5 m 1 . 515 m . 7 5 7 5 m 2 . 34 m A B θ If a wave pulse is sent from point A , how long does it take to travel to point B ? Correct answer: 36 . 7707 ms (tolerance ± 1 %). Explanation: Given : m = 15 . 9 g = 0 . 0159 kg , M = 1 . 4 kg , L = 3 . 03 m , L 2 = 1 . 515 m , L 4 = 0 . 7575 m , and D = 2 . 34 m . M M L 4 L 2 L 4 D A B θ θ d d Observing the lengths, 2 d + L 2 = D 4 d + L = 2 D d = 2 D- L 4 and cos θ = d L 4 = 4 d L = 2 D- L L , so θ = cos − 1 bracketleftbigg 2 D L- 1 bracketrightbigg = cos − 1 bracketleftbigg 2 (2 . 34 m) 3 . 03 m- 1 bracketrightbigg = 57 . 0058 ◦ ....
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HW12 - homework 12 – GAUTHIER JOSEPH – Due 1:00 am 1...

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