Find the highest frequency (rounded to the nearest Hz) for parts a and b *****(t

Question

Find the highest frequency (rounded to the nearest Hz) for parts a and b *****(the answers are not 245 and 294 Hz)

What frequencies will a 1.75 m long tube produce in the audible range (20 Hz - 20,000 Hz) at 19.0°C for the following cases? (a) the tube is closed at one end lowest frequency 49 second lowest frequency 147 highest frequency (rounded to the nearest Hz) Hz Hz (b) the tube is open at both ends lowest frequency 98 second lowest frequency 196 highest frequency (rounded to the nearest Hz) Hz Hz X Hz

Explanation / Answer

a) we know, in a closed pipe. f = n*(v/(4*L)) (where, n = 1,3,5,...)

let highest frquency, fmax = n*f_lowest ( here , n =1,3,5,7,9,...)

n = fmax/f_lowest

= 20000/49

= 408

so nearest odd number is 407

so,

fmax = 407*f_lowest

= 407*49

= 19943 Hz

b) we know, in an open pipe. f = n*(v/(2*L)) (where, n = 1,2,3,4,5,...)

let highest frquency, fmax = n*f_lowest ( here , n =1,2,3,4,5,...)

n = fmax/f_lowest

= 20000/98

= 204.08

so nearest integre is 204

so,

fmax = 204*f_lowest

= 204*98

= 19992 Hz

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