The relationship between the length of the tube and the pitch of the instrument can be expressed by the following formula:
```
f = v/λ
```
where:
* f is the frequency of the sound in hertz (Hz)
* v is the speed of sound in meters per second (m/s)
* λ is the wavelength of the sound in meters (m)
The speed of sound in air is approximately 343 m/s. The wavelength of the sound is equal to the length of the air column that vibrates when the instrument is played.
For example, a trumpet has a tube that is approximately 1.3 meters long. The wavelength of the sound that is produced by a trumpet is therefore approximately 1.3 meters. The frequency of the sound that is produced by a trumpet is therefore approximately 261 Hz, which is the pitch of the note C4.
The same principle applies to all other tube brass instruments. The longer the tube, the lower the pitch of the instrument. This is why tubas are lower in pitch than trumpets.
The length of the tube is not the only factor that affects the pitch of a brass instrument. The shape of the bell, the size of the mouthpiece, and the tension of the valves all also play a role. However, the length of the tube is the most important factor in determining the pitch of a brass instrument.