Question

The pan flute is a musical instrument consisting of a number of closed-end tubes of different lengths. When the musician blows over the open ends, each tube plays a different note. The longest pipe is 0.31 m long.

What is the frequency of the note it plays? Assume room temperature of 20∘C.

Answer 1

f = 276.6 Hz

Step-by-step explanation:

This musical instrument can be approximated to a tube system where each tube has one end open and the other closed.

In the closed part there is a node and in the open part a belly or antinode. Therefore the wavelength is

L = λ/ 4

speed is related to wavelength and frequency

v = λ f

λ = v / f

we substitute

L = v / 4f

f = v / 4L

the speed of sound at 20ºC is

v = 343 m / s

let's calculate

f =
`(343 )/(4 \ 0.31)`

f = 276.6 Hz