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Exam 4 Solutions

# Exam 4 Solutions - midterm 04 – ALIBHAI ZAHID – Due May...

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Unformatted text preview: midterm 04 – ALIBHAI, ZAHID – Due: May 2 2007, 11:00 pm 1 Question 1 part 1 of 1 10 points The diagrams below show different stand- ing waves on a 49 . 5 cm string. Which of these waves has a 33 cm wave- length? 1. 2. 3. 4. 5. 6. 7. 8. correct 9. Explanation: A standing wave on a string has nodes where the string does not vibrate; these nodes are spaced half-wavelength from each other: x = 0 , x 1 = λ 2 , x 2 = 2 × λ 2 , x 3 = 3 × λ 2 , x 4 = 4 × λ 2 ,.... A fixed end of the string cannot vibrate, so it must be a node of the standing wave. For the string fixed at both ends, both ends must be nodes of the wave, hence L = n × λ 2 , n = 1 , 2 , 3 ,..., (1) where n is the number of vibrating segments of the string. More precisely, the wave on the string has n antinodes and n + 1 nodes: One node at each end of the string, plus n- 1 nodes in the middle. The wave in question has wavelength λ = 33 cm on a string of length L = 49 . 5 cm, hence according to eq. (1), n = L λ/ 2 = 49 . 5 cm (33 cm) / 2 = 3 , which means the wave has 3 antinodes and 4 nodes: One at each end, and 2 in the middle. midterm 04 – ALIBHAI, ZAHID – Due: May 2 2007, 11:00 pm 2 In other words, it looks like . Question 2 part 1 of 1 10 points Sound in air can best be described as which of the following type of wave? 1. Torsional 2. Transverse 3. Polarized 4. Electromagnetic 5. Longitudinal correct Explanation: A sound wave in the air is propagated by the oscillation of air molecules. It is best described as a longitudinal wave. Question 3 part 1 of 1 10 points The sound of a man shouting at the top of his lungs from a rather large distance away from your ear has loudness of only 20 decibels. What would be the decibel level of four men shouting at the top of their (equally powerful) lungs from the same distance away from you ear? Assume that there is no interference from superposed waves. 1. β 4 = 160 dB 2. β 4 = 26 dB correct 3. β 4 = 80 dB 4. β 4 = 6 dB 5. β 4 = 14 dB 6. β 4 = 5 dB 7. β 4 = 20 dB 8. β 4 = 40 dB 9. β 4 = 60 dB 10. β 4 = 10 dB Explanation: The decibel level β is a logarithmic measure of sound intensity I : β = 10 log 10 parenleftbigg I I parenrightbigg . Since we have assumed that there is no in- terference from superposed waves, four men shouting together produce a sound intensity four times greater than that of just one man ( I 4 = 4 I 1 ), so β 4 = 10 log 10 4 I 1 I = 10 log 10 parenleftbigg I 1 I parenrightbigg + 10 log 10 (4) = β 1 + 10 log 10(4) = 20 dB + 10 log 10 (4) = 26 . 0206 dB . Question 4 part 1 of 1 10 points A(n) 0 . 323 kg mass is attached to a spring and undergoes simple harmonic motion with a period of 0 . 0526 s . The total energy of the system is 4 . 4 J ....
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Exam 4 Solutions - midterm 04 – ALIBHAI ZAHID – Due May...

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