Question

The clarinet is an instrument with a closed end at one end (by the reed) and an open end at the other.

1. (a) The clarinet has a length of 60 cm. What is the fundamental frequency of the clarinet if simply played as a tube like this?

2. (b) A clarinet has a register key which allows its third order harmonics to be played. What frequency sound would this produce? Sketch the pressure variations of the third order harmonic in the clarinet, indicating which end is the reed.

3. (c) A flute is about as long as a clarinet, yet a flute typically plays higher notes than the clarinet does. A flute is open at both ends. Explain why the pitch of the flute is typically higher than that of the clarinet.

Answer 1

(a)A clarinet is a pipe closed at one end and open at the other. Hence it is a closed ended tube with pressure at the open end equal to the atmospheric pressure and the pressure at the closed end(mouth piece) being the maximum. The clarinet can produce a fundamental wave of wavelength that is four times the length of the clarinet. Therefore . Therefore, . the velocity of sound in air is 340m/s. Therfore the fundamental frequency of the clarinet is .

(b) The frequency of the harmonics are integral multiples of fundamental frequency. The frequency of the third order harmonics is thrice that of the fundamental frequency. Therefore, .

(c) The Fundamental wavwlegth of the flute which is an open ended pipe is twice that of its length. Considering a flute and clarinet of the same length, we have

Fundamental frequency of the clarinet whereas the fundamental frequency of the flute is which is higher than that of the clarinet. Hence the pitch which is nothing but the frequency of the flute is higher.

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