Question

,50, the standing wave shown in Figure 7-30 is set up on a string, The string has length of s t and At time locity 50 ft/s. What are the frequencies of the first eight allowed normal modes on this string- a)25,50, 75, , . . , 17.5, 20.0 Hz b) 2.5,75, 12.5,... ,32.5, 375 Hz c) 5, 10, 15,,35, 40 Hz d) 5, 15, 25, .,65, 75 Hz e) 10, 20, 30, .,80 Hz lex wave shown at t-0 in Figure 7-30 symmetric, antisymmetric, or of mixed symmetry? 8. Is the complex IGURE 7-30 Wave shape on a string tied at both ends at time t 0. The length of the string is L-5 ft. The propagation velocity of waves on the string is D-50 ft/s 9. According to Fourier's theorem, which of the frequencies in Question 7 will you likely need to add to make up the complex wave of Figure 7-30? a) 2.5, 5.0, 7.5,.. ., Hz b) 2.5,7.5, 12.5,.., Hz 5,10, 15,. .., Hz d)5,15, 25,..., Hz e) 10, 20, 30,..., Hz 10. Suppose that, in order of increasing frequency, the relative amplitudes of the first four constituent sinusoidal components of the wave of Figure 7-30 are 1,05,03, and O1. Plot a frequency spectrum for the complex wave 11. Redo Question 7, assuming that the length of the string is now L- 10 ft. and everything else is the same. The answer set given in 7 will still apply. answer set given in 9 will still apply frequency spectrum on the same sheet of paper as is the same except the length of the string, which is now L- 10 ft. The 12. Redo Question 9 if everything same except length of the string is now L - 10 ft. Put the 13. Redo Question 10 if everything is the same except that the that of Question 10. Explain as precisely as you can what wave of Figure 7-30 as you increase the length happens to the frequency spectrum o of the strin he fequecspecrum of the omplex standing except now use the values, 0.2, 1,0.4, and 0.2 for the amplitudes of the first four constituent fec needed in Questi 14. Do the ed in Question 10. With regard to the frequency spectrum of this second complex wave, can reason why the relative amplitude of the second constituent sinusoidal wave is same operations as in Questions 7 through 10 for the standing complex wave than the relative larger amplitudes of the other constituent sinusoidal waves?

Answer 1

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