Full question is in the description.

Question

1. What is the fundamental

frequency produced by a

vibrating air column 2.50 m

long and open at one end? The

speed of sound is 344 m/s.

2. What is the frequency of the

first overtone that will be

produced by the air column

in question 1?

3. What harmonic is the

overtone in question 2?

Answer 1

Let v = 344 m/s be the speed of sound.

All the possible vibrations will have a node at the closed end,

while the open end will have the maximum oscillation.

Therefore the lowest, fundamental, frequency corresponds to the wave

where only 1/4 of the wavelength fits into the column.

Therefore the wavelength λ = 10m.

The fundamental frequency, f₀, is then calculated using the formula

f₀ = v/λ = 344/10 = 34.4 Hz

The next higher possible frequency fits a half-wavelength into the column

plus a quarter.

In other words, it fits three time more of into the column than the above.

(If you could draw a picture it would be helpful.)

Therefore the next possible frequency is

f₁ = 3f₀

The next higher possible frequency fits two half-wavelength into the column

plus a quarter.

In other words, it fits five time more of into the column than the fundamental.

Therefore the next possible frequency is

f₂ = 5f₀

And so on.

Questions 2. and 3. are about terminology and about counting overtones and harmonics.

Normal terminology considers the fundamental frequency one of the harmonics,

but not one of the overtones.

In question 2. it is not clear to me what the word "first" means.

Using informal English "first overtone" would refer to the above f₁.

But some technical terminology calls f₁ the third overtone.