I already asked this question but not sure how to ask for more help because the

Question

I already asked this question but not sure how to ask for more help because the first answer I got was not detailed or answered in full. So if I could get some detailed help.

Part 1
A spaceships lands on a new planet. The crew decides to measure the speed of sound in the atmosphere. Taking a tube with a length of 50 cm, they find that one resonant freqency occurs at 2,520 Hz, and the next resonant frequency at 2,940 Hz. What is the speed of sound? What is the number of each harmonic? What type of pipe is the crew using (open-open, closed-closed, or open-closed ended)?

Part 2
The crew from part 1 lands on another planet and repeat the experiment. This time they find frequencies of 1,620 Hz and 1,980 Hz. What is the speed of the sound? What is the number of each harmoic? What type of pipe is the crew using this time (open-open, closed-closed, or open-closed ended)?

for part 1, i got 420 Hz as the fundamental frequency so it would make2520 Hz = 5th harmonic and 1980 Hz as 6th harmonic. and speed is 420 m/s. I think it would be an open-open tube. for part 2, i got fundamental frequency as 180 Hz so it would make 1620 Hz =9th harmonic and 1980 Hz as 11th harmonic, since they are odd numbered it would be a open/closed pipe. and speed of sound is 360 m/s.

I need to know the correct way of how to get the answers if they are right. I kinda of reasoned the answers. Any help to show in detail how to get each part of the answer

Explanation / Answer

Part 1:

fundamental frequency = 2940-2520 = 420hz

for 2520hz its harmonic number is (2520/420) = 6

2100hz is the 5th harmonic and 1980 hz is considered as the 4th harmonic, 840hz is the second harmonic, 1260 is the 3rd harmonic and so on.

frequency = velocity/(2*Tube length)

hence velocity = 420*2*0.5

= 420m/s

the tube is open open tube

Part 2:

fundamental frequency = 1980-1620 = 360hz

for 2520hz its harmonic number is (1980/360) = 5.5 it is considered to be 5th harmonic

1620 hz is considered as the 4rd harmonic, 720hz is the second harmonic, 1080 is the 3rd harmonic and so on.

frequency = velocity/(2*Tube length)

hence velocity = 360*2*0.5

= 360m/s

the tube is also open open tube

since

for 2520hz obtained in part 1

number of harmonics are 2520/420 = 6

consider for the same frequency in part 2

number of harmonics are 2520/360 = 7

hence the tubes are same and they are open

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