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

the total distance that martina travels that day is

(distance from home to mom's office) plus (distance from mom's office to school)

plus (distance from school to library) plus (distance from library to friend's house)

plus (distance from friend's house to martina's house).

(we don't know what any of these distance actually is.)