HW34 - homework 34 PAPAGEORGE MATT Due 4:00 am Explanation...

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homework 34 – PAPAGEORGE, MATT – Due: Apr 22 2008, 4:00 am 1 Question 1, chap 16, sect 4. part 1 of 2 10 points A standing wave of frequency 5 hertz is set up on a string 2 meters long with nodes at both ends and in the center, as shown. 2 meters Find the speed at which waves propagate on the string. 1. 10 m / s correct 2. 2 . 5 m / s 3. 0 . 4 m / s 4. 20 m / s 5. 5 m / s Explanation: Let : f = 5 Hz and λ = 2 m . The wavelength is λ = 2 m, so the wave speed is | vectorv | = f λ = (5 Hz)(2 m) = 10 m/s . Question 2, chap 16, sect 4. part 2 of 2 10 points Find the fundamental frequency of vibra- tion of the string. 1. 10 Hz 2. 5 Hz 3. 2 . 5 Hz correct 4. 7 . 5 Hz 5. 1 Hz Explanation: 2 meters The fundamental wave has only two nodes at the ends, so its wavelength is λ = 4 m and the fundamental frequency is f = v λ = 10 m / s 4 m = 2.5 Hz . Question 3, chap 16, sect 4. part 1 of 4 10 points To demonstrate standing waves, one end of a string is attached to a tuning fork with frequency 270 Hz. The other end of the string passes over a pulley and is connected to a suspended mass M , as shown. The value of M is such that the stand- ing wave pattern has four loops “anti-nodes”. The length of the string from the tuning fork to the point where the string touches the top of the pulley is 1 . 9 m. The linear density of the string is 8 × 10 - 5 kg / m, and remains constant throughout the experiment. The acceleration of gravity is 9 . 8 m / s 2 . M Tuning Fork Pulley 1 . 9 m 270 Hz Determine the wavelength of the standing wave. Correct answer: 0 . 95 m (tolerance ± 1 %). Explanation: Let : n = 4 ,
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homework 34 – PAPAGEORGE, MATT – Due: Apr 22 2008, 4:00 am 2 f = 270 Hz , L = 1 . 9 m , and μ = 8 × 10 - 5 kg / m .
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