Unformatted text preview: Waves Homework Problems Michael Fowler 3/29/07 1. Sketch the appearance of a single transverse wave pulse traveling down a string at some instant, and below it sketch the velocit ies of the small segments of string at that same instant. 2. Given that the note middle C corresponds to a frequency of 262 Hz., find the length of an organ pipe having this as its fundamental (lowest frequency) note (a) if both ends of the pipe are open (b) if one end is closed, one end open. (c) What note would the organ pipe sound if filled with helium gas? (the bulk modulus is the same as for air). 3. Humans can only hear sounds in the frequency range 20 Hz to 20,000 Hz. What would be the lo ngest and shortest organ pipes there is any po int in manufacturing? 4. The speed of sound in water is about 1.5 km/sec. (a) Figure out from that the bulk modulus of water. (b) How compressed in vo lume is the water at the bottom of the deepest ocean? 5. A piston (a speaker) at one end of a long tube is oscillat ing at 262 Hz with an amplitude of 0.2mm. The piston is circular, with a diameter 5 cm. (a) Find the maximum pressure variat ion at the plate. (b) What is the average power output of the plate? (c) How much energy is there in one meter of the traveling wave as it goes down the tube? 6. Assume a steel piano wire is 50 cm long and weighs 3 grams. It is held at a tension of 1,000N. (a) What is its fundamental frequency? (b) What is the wavelength of that sound in air? (c) How does the speed of a traveling wave in the steel piano wire co mpare to the speed of sound in air? The speed of sound in so lid steel is far greater than the speed of sound in air. Does that contradict your finding for the wire? Explain why or why not. 7. A string under tensio n is pulled aside in the middle so it has the fo llowing Vshape: Describe with a series of sketches the subsequent mot ion of the string. (Hint: study the spreadsheet addit ion of two traveling sine waves to form a standing wave. The init ial string configurat ion here is half a wave length of a zigzag wave.) ...
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- Fall '07
- Work, steel piano wire, transverse wave pulse, lo ngest, string configurat ion, bulk modulus, spreadsheet addit ion