v = f fn = nf1  = 5558 m 343 = 5558(f) f = Hz 325th harmonic

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v = f fn = nf1  = 5558 m 343 = 5558(f) f = 0.0617 Hz 325th harmonic Given: L = 2779 m n = 1 (fundamental frequency) v = 343 m/s 1) (open air column) a) v = f  = 5558 m 343 = 5558(f) f = 0.0617 Hz b) fn = nf1 325th harmonic 20 = n(0.0167)

v = f v = f  = 0.96 m 343 = 0.96(f) f = 357.3 Hz = 476.4 Hz Given: L = 48 cm = 0.48 m n = 1 (fundamental frequency) v = 343 m/s 2) (open air column) v = f  = 0.96 m 343 = 0.96(f) f = 357.3 Hz = 476.4 Hz L = 0.36 m v = f 12 cm from the end 343 = (476.4)  = 0.72 m

v = f open pipe f2 = 306.2 Hz; f3 = 459.3 Hz; f4 = 612.4 Hz 3) Given: L = 112 cm = 1.12m n = 1 (fundamental frequency) v = 343 m/s open pipe f2 = 306.2 Hz; f3 = 459.3 Hz; f4 = 612.4 Hz (open air column) closed pipe f3 = 229.8 Hz; f5 = 383.0 Hz; f7 = 536.2 Hz open = 2.24 m (closed air column) closed = 4.48 m v = f open pipe f1 = 153.1 Hz 343 = 2.24(f) closed pipe f1 = 76.6 Hz 343 = 4.48(f) fn = nf1 open pipe next three harmonics = 2, 3, 4 closed pipe next three harmonics = 3, 5, 7

60 Hz 100 Hz 140 Hz. f3 f5 f7 20 Hz These differ by how much ? 40 Hz 4) (closed air column) These differ by how much ? 40 Hz 60 Hz 100 Hz 140 Hz. f3 f5 f7 These differ by how much ? 40 Hz By how much less would you expect the harmonic before 60 Hz to be? 40 Hz What is the frequency of the harmonic before 60 Hz? I know this is the fundamental frequency since 40 Hz below this would be negative 20 Hz

closed air column 88 Hz 264 Hz 440 Hz 616 Hz. f3 f5 f7 88 Hz 5) 88 Hz These differ by how much ? 176 Hz 264 Hz 440 Hz 616 Hz. f3 f5 f7 These differ by how much ? 176 Hz By how much less would you expect the harmonic before 264 Hz to be? 176 Hz What is the frequency of the harmonic before 264 Hz? I know this is the fundamental frequency since 176 Hz below this would be negative 88 Hz

v = f v = f 343 = (262)  = 1.309 m 337 = 1.309(f) L = 65.5 cm Given: f = 262 Hz n = 1 (fundamental frequency) v = 343 m/s 6) (open air column) v = f 343 = (262)  = 1.309 m v = f 337 = 1.309(f) L = 65.5 cm f = 257.4 Hz

v = f 343 = (294)  = 1.16 m L = 0.58 m 7.5 cm from the end Given: f = 294 Hz n = 1 (fundamental frequency) v = 343 m/s 7) (open air column) v = f 343 = (294)  = 1.16 m L = 0.58 m 7.5 cm from the end