Question

The contrabassoon is the wind instrument capable of sounding the lowest pitch in an orchestra. It is folded over several times to fit its impressive 18 ft length into a reasonable size instrument.The actual fundamental frequency of the contrabassoon is 27.5 Hz , which should be different from your answer in part A. This means the model of the instrument as an open-closed tube is a bit too simple. But if you insist on using that model, what is the "effective length" of the instrument?

Answer 1

3.12 m

Step-by-step explanation:

The fundamental frequency of an open-closed tube is given by

`f_1 = (v)/(4L)`

where

f1 is the fundamental frequency

v is the speed of sound in air (343 m/s)

L is the length of the tube

If we use the model mentioned, we can consider L to be the effective length of the instrument. This means we can re-arrange the formula and use the fundamental frequency, f1 = 27.5 Hz, to find L:

`L=(v)/(4 f_1)=(343 m/s)/(4(27.5 Hz))=3.12 m`