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HW33 - homework 33 PAPAGEORGE MATT Due 4:00 am Question 1...

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homework 33 – PAPAGEORGE, MATT – Due: Apr 19 2008, 4:00 am 1 Question 1, chap 16, sect 2. part 1 of 2 10 points A steel piano wire is 0 . 7 m long and has a mass of 60 g. It is stretched with a tension of 600 N. What is the speed of transverse waves on the wire? Correct answer: 83 . 666 m / s (tolerance ± 1 %). Explanation: Let : F = 600 N , L = 0 . 7 m , and m = 60 g = 0 . 06 kg . The speed of transverse waves on the wire is given by v = radicalBigg F μ = radicaltp radicalvertex radicalvertex radicalbt F m L = radicalbigg F L m = radicalBigg (600 N) (0 . 7 m) 0 . 06 kg = 83 . 666 m / s . Question 2, chap 16, sect 2. part 2 of 2 10 points To reduce the wave speed by a factor of 2 without changing the tension, what mass of copper wire would have to be wrapped around the steel wire? Correct answer: 180 g (tolerance ± 1 %). Explanation: Let : v v = 2 , and m = 60 g = 0 . 06 kg . The new wave speed will be v = radicalbigg F L m radicalbigg 1 m , so v v = 2 = radicalbigg m m m = 4 m . The amount of copper wire required is Δ m = m - m = 3 m = 3 (0 . 06 kg) = 180 g . Question 3, chap 16, sect 2. part 1 of 1 10 points Tension is maintained in a string as in the figure. The observed wave speed is 25 m / s when the suspended mass is 2 . 8 kg . The acceleration of gravity is 9 . 8 m / s 2 . 2 . 8 kg What is the wave speed when the suspended mass is 3 kg? Correct answer: 25 . 8775 m / s (tolerance ± 1 %). Explanation: Let : m 1 = 2 . 8 kg , m 2 = 3 kg , and v 1 = 25 m / s . The linear density is v 1 = radicalBigg F μ , so μ = F v 2 1 (1) = m 1 g v 2 1
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homework 33 – PAPAGEORGE, MATT – Due: Apr 19 2008, 4:00 am 2 = (2 . 8 kg) (9 . 8 m / s 2 ) (25 m / s) 2 = 0 . 043904 kg / m . The velocity is v 2 = radicalBigg F μ , so v 1 = radicalbigg m 2 g μ (2) = radicalBigg (3 kg) (9 . 8 m / s 2 ) 0 . 043904 kg / m = 25 . 8775 m / s . AlternateSolution: Plugging μ from Eq. 1 into Eq. 2, we have v 1 = radicalbigg m 2 g μ (2) = radicalBigg m 2 g v 2 1 m 1 g = v 1 radicalbigg m 2 m 1 (3) = (25 m / s) radicalBigg (3 kg) (2 . 8 kg) = 25 . 8775 m / s . Question 4, chap 16, sect 2. part 1 of 3 10 points A sonar signal of frequency 2 . 05 × 10 6 Hz has a wavelength of 1 . 68 mm in water.
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