An air-filled pipe is found to have successive harmonics at 800 {\rm Hz} , 1120 {\rm Hz} , and 1440 {\rm Hz} . It is unknown whether harmonics below 800 {\rm Hz} and above 1440 {\rm Hz} exist in the pipe. What is the length of the pipe?

The length of the pipe is 53.59 cm

Explanation:

Given;

successive harmonics in the air-filled pipe = 800 Hz, 1120 Hz and 1440 Hz

For closed pipes, frequency = nv/4L

where n is odd numbers

the harmonics are F₀, 3F₀, 5F₀, 7F₀, 9F₀ etc

the difference between successive harmonic is 2F₀

2F₀ = 1120 Hz - 800 Hz

2F₀ = 320

F₀ = 320 / 2

F₀ = 160 Hz

Fundamental frequency (F₀) is given as;

F₀ = v/4L

Where;

v is the velocity of sound = 343 m/s

L = v/4F₀

L = 343 / (4 x 160)

L = 0.5359 m

L = 53.59 cm

Therefore, the length of the pipe is 53.59 cm

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