Question

An organ pipe is 120 cm long. What are the fundamental and first three audible overtones if the pipe is (a) closed at one end, and (b) open at both ends?

1st overtone(2nd harmonic) if closed at one end?

Fundamental(1st harmonic) if closed at one end?

Fundamental(1st harmonic) if open at both ends?

2nd overtone(5th harmonic) if closed at one end?

2nd overtone(4th harmonic) if closed at one end?

1st overtone(2nd harmonic) if open at both ends?

3rd overtone(7th harmonic) if closed at one end?

2nd overtone(3rd harmonic) if open at both ends?

3rd overtone(4th harmonic) if open at both ends?

1st overtone(3rd harmonic) if closed at one end?

Answer 1

as v=340m/s

pipe is closed at one end

closed pipe: f=(2n-1)v/4L , (v=340m/s , L=1.20m)

n=1: f=(2*1-1)*340/(4*1.20) = 70.83[Hz] 1st.harmonic, fundamental f.

n=2: f=(2*2-1)*340/(4*1.20) = 212.5[Hz] 3rd.harmonic, 1st.overtone.

n=3: f=(2*3-1)*340/(4*1.20) = 354.2[Hz] 5th.harmonic, 2nd.overtone.

n=4: f=(2*4-1)*340/(4*1.20) = 495.8[Hz] 7th.harmonic, 3rd.overtone.

pipe is open at both ends

open pipe; f=nv/2L , (v=340m/s ,L=1.20m)

n=1: f=1*340/(2*1.20) = 141.67[Hz] 1st.harmonic, fundamental.

n=2: f=2*340/(2*1.20) = 283.33[Hz] 2nd.harmonic, 1st.overtone.

n=3: f=3*340/(2*1.20) = 425[Hz] 3rd.harmonic, 2nd.overtone.

n=4: f=4*340/(2*1.20) = 566.67[Hz] 4th.harmonic, 3rd.overtone.