Question

(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`.

Answer 1

(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`