Question

You are designing a four note pan flute. The flute tubes are 12.5cm in diameter. It is to play root (A=880Hz), Maj. 3rd, P4, and P5. How long do you make the tubes?

Answer 1

A flute is a one end closed pipe.

The frequencies of the resonant modes is given by the length of the tube.

The equation for resonant frequencies is given by

Where L is the length of the tube,

c is the speed of sound in air = 343 m/s

and n is an integer.

Here, we need 4 frequencies

• A = 880 Hz
• 3rd Maj (E) = 880*5/4 = 1100 Hz
• P4 = 880*4/3 = 1173.3 Hz
• P5 = 880*3/2 = 1320 Hz

We have to find the lengths of tubes for these resonant frequencies.

The length of fundamental frequency (n = 1) for the frequencies is given by

Thus,

For A, L = 343/(2*880) = 0.19488 m = 19.49 cm

For E, L = 343/(2*1100) = 0.1559 m = 15.59 cm

For P4, L = 343/(2*1173.3) = 0.1462 m = 14.62 cm

For P5, L = 343/(2*1320) = 0.1299 m = 12.99 cm

Since all these lengths are larger than the diameter of the tube, these lengths can be used to produce the frequencies.