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(a) A cylindrical metal tube has a length of `50 cm` and is open at both ends. Find the frequencies between `1000 Hz` and `2000 Hz` at which the air is `340 m//s`. (b) Find the greatest length of an organ pipe open at both ends that will have its fundamental frequency in the normal hearing range `(20 - 20000 Hz)`. Speed of sound in air `= 340 m//s`. (c) Two successive resonance frequencies in an open organ pipe are `1944 Hz` and `2592 Hz`. Find the length of the tube. The speed of sound in air is `324 m//s`. |
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Answer» (a) For open pipe, fundamental frequency `f = (v)/(2l) = (340)/(2 xx 0.5) = 340 Hz` Possible frequencies of open pipe `= nf, n = 1,2,3,…` `340,680,1020,1360,1700,2040 Hz` Frequencies between `1000` and `2000 Hz` `= 1020 Hz,1360 Hz,1700 Hz` (b) `f = (v)/(2l)` `l = (v)/(f)` , l will be maximum if `f` is minimum `l_(max) = (340)/(2 xx 20) = 8.5 m` (c) The difference in successive frequencies of a pipe (open or closed) `= (v)/(2l)` `2592 - 1944 = (324)/(2l)` `l = (1)/(4) m = 0.25 m` |
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