Question

A clarinet is basically sealed at one end (you blow into a very narrow hole), but open at the other. A flute is open at both ends. If you have a clarinet and flute of equal lengths, and play the fundamental

a. The flute will sound lower.

b. The clarinet will sound lower.

c. They will have identical pitch.

d. Not enough information.

Answer 1

Clarinet is a closed pipe of length L( say). The clarinet can support only those vibrations for which the closed end is a node while the open end it is an antinode. For fundamental there are one node and one antinode. If fundamental frequency is f_{​​​​​​1} and corresponding wavelength ₁ then ₁ =4* L.

And f_{​​​​​​1}​​ = V/₁ = V/(4*L).

Flute is a open pipe of same length L. The flute can support only those waves for which antinodes are produced at both of its open end. For fundamental there are two antinodes and one node. If fundamental frequency is f_{​​​​​} and corresponding wavelength then = 2*L.

And f = V/ = V/(2*L).

So, f = 2* f_{​​​​​​1}​​​ i.e. fundamental frequency of flute is double of the fundamental frequency of the clarinet of same length. So, clarinet have lower sound.

Ans) b. The clarinet will sound lower.