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(a) What are the three longest wavelengths for a standing wave on a 240-cm-long string that is fixed at both ends?
(b) The frequency of the second longest wavelength is 50Hz. what is the frequency of the third longest wavelength?
(c) If you now tightly pinch the string 80cm away from the left end, and only allow the right half of the string oscillates, what is the new fundamental frequency and its corresponding wavelength?
(d) If instead of pinching, you rest your finger lightly at the same spot, what are the two lowest frequencies that the string can vibrate in?
Show all the steps in the mechanism for the following reaction, When benzene is mixed with deuterated sulfuric acid, deuterium is slowly incorporated onto the ring. Show the mechanism for this reaction and explain how this relates the sulfonation of ..
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