High Notes on the Tuba

As an experienced tubist, I have been practicing bettering the quality of my higher range for years now, but it is still a challenge. The challenging aspect of playing clear high notes through a tuba can be attributed to physics. The higher the pitch, the higher the frequency of the sound waves. To increase the frequency of the sound waves, one must increase the speed of the air through the tuba. To do so, you increase the pressure of the air in the mouthpiece by pressing your lips close together to generate a fast stream of air. This seems simple enough, so what's the challenge. As frequency is proportional to velocity, it is inversely proportional to length. Therefore, even though the speed of the air is increasing, the tuba is 16 feet of brass tubing, one of the longest instruments ever made. This makes generating a higher pitch by increasing the frequency extremely hard. The pressure in the mouthpiece need to increase an incredible amount due to the length of the instrument. So I suppose I'll just have to give up on the tuba because I can never defy physics.