26.(I) What would you estimate for the length of a bass clarinet,assuming that it is modeled as a closed tube and that thelowest note that it can play is a whose frequency is 69 Hz? 27.(I) The A string on a violin has a fundamental frequency of440 Hz. The length of the vibrating portion is 32 cm, and ithas mass 0.35 g. Under what tension must the string be placed? 28. (I) An organ pipe is 116 cm long. Determine the fundamental and first three audible overtones if the pipe is ( a ) closed at one end, and ( b ) open at both ends. 29.(I) (a) What resonant frequency would you expect fromblowing across the top of an empty soda bottle that is 24 cmdeep, if you assumed it was a closed tube? (b) How wouldthat change if it was one-third full of soda? 30.(I) If you were to build a pipe organ with open-tube pipesspanning the range of human hearing (20 Hz to 20 kHz),what would be the range of the lengths of pipes required? 31.(II) A tight guitar string has a frequency of 540 Hz as itsthird harmonic. What will be its fundamental frequency ifit is fingered at a length of only 70%of its original length? 32. (II) Estimate the frequency of the “sound of the ocean” when you put your ear very near a 15-cm-diameter sea- shell (Fig. 12 – 35). D 41.(II) How many overtones are present within the audiblerange for a 2.18-m-long organ pipe at 20°C (a) if it is open,and (b) if it is closed? 42. (II) Determine the fundamental and first overtone frequen- cies when you are in a 9.0-m-long hallway with all doors closed. Model the hallway as a tube closed at both ends. 43. (III) When a player’s finger presses a guitar string down onto a fret, the length of the vibrating portion of the string is shortened, thereby increasing the string’s fundamental frequency (see Fig.12 – 36). The string’s tension and mass per unit length remain unchanged. If the unfingered length of the string is determine the positions x of the first six frets, if each fret raises the pitch of the fundamental by one musical note compared to the neighboring fret. On the equally tempered chromatic scale, the ratio of frequencies of neighboring notes is 2 1 12 . l = 75.0 cm, l 75.0 cm x FIGURE 12–36 Problem 43. FIGURE 12–35 Problem 32. 33. (II) An unfingered guitar string is 0.68 m long and is tuned to play E above middle C (330 Hz). ( a ) How far from the end of this string must a fret (and your finger) be placed to play A above middle C (440 Hz)? ( b ) What is the wave- length on the string of this 440-Hz wave? ( c ) What are the frequency and wavelength of the sound wave produced in air at 22°C by this fingered string? 34. (II) ( a ) Determine the length of an open organ pipe that emits middle C (262 Hz) when the temperature is 18°C. ( b ) What are the wavelength and frequency of the funda- mental standing wave in the tube? ( c ) What are and f in the traveling sound wave produced in the outside air?
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