Question

What frequencies (in Hz) will a 1.90 m long tube produce in the audible range (20 Hz - 20,000 Hz) at 18.0°C for the following cases? (a) the tube is closed at one end Hz Hz Hz lowest frequency second lowest frequency highest frequency (rounded to the nearest Hz) (b) the tube is open at both ends Hz Hz Hz lowest frequency second lowest frequency highest frequency (rounded to the nearest Hz)

Answer 1

(a) The frequency of the tube when it is closed at one end is, f - (2n+1)v 42 The lowest frequency is, +_(2(0)+1)(343 m/s) 4(1.9 m) = 45.13 Hz fi = The second lowest frequency is, r_(2(1)+1)(343 m/s) 4(1.9 m) = 135.39 Hz The maximum frequency is, Some - (2n+1)v 41 20000 Hz - (2n+1)(343 m/s) 4(1.9 m) 2n+1=443.15 n=221 If n= 220 then the frequency becomes the highest frequency. (2(220)+1)(343 m/s) I highest 4(1.9 m) =19903.03 Hz

(b) The frequency of the tube when it is open at both the ends is, fumy The lowest frequency is, f_(1)(343 m/s) 2(1.9 m) = 90.26 Hz The second lowest frequency is, f_(2)(343 m/s) 2(1.9 m) = 180.53 Hz The maximum frequency is, 21 fmser = 2 (343 m/s) 20000 Hz= 2(1.9 m) n=221 If n= 220 then the frequency becomes the highest frequency. (220) (343 m/s) ghes 2(1.9 m) = 19857.89 Hz