Q. Show how the frequency is related to the length of a pipewith both ends open

Question

Q. Show how the frequency is related to the length of a pipewith both ends open and one end open. (Hint: use sketches of theharmonics separatly for each pipe). At least show three consecutiveharmonics for each tube. a) Organ pipe A, with one end open, has a fundamentalfrequency of 200 Hz. The third harmonic of organ pipe B, with bothends open, has the same frequency as the fifth harmonic of pipeA. b) How long are pipe A and pipe B? Q. Show how the frequency is related to the length of a pipewith both ends open and one end open. (Hint: use sketches of theharmonics separatly for each pipe). At least show three consecutiveharmonics for each tube. a) Organ pipe A, with one end open, has a fundamentalfrequency of 200 Hz. The third harmonic of organ pipe B, with bothends open, has the same frequency as the fifth harmonic of pipeA. b) How long are pipe A and pipe B?

Explanation / Answer

Q. Show how the frequency is related to the length of a pipewith both ends open and one end open. (Hint: use sketches of theharmonics separately for each pipe). At least show threeconsecutive harmonics for each tube.
for open pipe
n=V/2l fundamental frequency
for second harmonic
n1=2V/2l
for third harmonic n2=3V/2l
for fourth harmonic n3=4V/2l

for closed pipe
n=V/4l fundamental frequency
for second harmonic
n1=3V/4l
for third harmonic n2=5V/4l
for fourth harmonic n3=7V/4l



a) Organ pipe A, with one end open, has a fundamentalfrequency of 200 Hz. The third harmonic of organ pipe B, with bothends open, has the same frequency as the fifth harmonic of pipeA.



b) How long are pipe A and pipe B?

V/4lA=200Hz=3V/2lB
assuming V=340m/sec
lA=0.425m=42.5cm

lB=2.55m

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