Question

An organ pipe is observed to produce 3 consecutive harmonics with frequencies of 189, 243 and 297 Hz. By how much does the tube need to be shortened so that the fundamental frequency is 60 Hz? The speed of sound is 343 m/s.

Answer 1

solution Ae We know that open organ Pipe We get all the harmonic (odd & Even) and close organ pipe only odd harmonic there for For open let nth harmonic in= 189 and (nul on hanminit fp+1) = 243 than - Futi- fn = Pi 243-189=f F = 54 ] is 100 = .358 for clore let nth honmonie fn = 189 and 1h+hth hamonic fin+1) = 243 S4 then 243-10g = 24 If = 27 ] So 27x7 = 10g 274 9 = 243

for given harmonic So our Jundamental requing frequeng is - H=27 H2 for clore Pire fi- I E linia 3.1759 m j fundamental frequency is z wave 2018 - fp = b 12 then 343 4x60 = 341 =1.4291m 240 So the need of shortened length ol= linitial -d Find = 31789 – 1.4291 = 1.7460 m Ang