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

answer: b.

explanation:

increasing transnational kinetic energy. because the transnational kinetic energy formula consists of only two variables, mass and velocity, increasing one of those properties is the only way to increase an object's transnational kinetic energy. increases to mass and velocity, however, do not have the same impact.