# How can I apply related rates to my IA on the flute? (Urgent)

## Recommended Posts

I am trying to do a Math HL calculus IA on the flute and my outline is due in two days. I started by measuring the distance to the first open hole for each note fingering and graphing it on the x axis with frequency of the notes on the y axis. This gave me a quadratic function that can be differentiated to find the change in frequency with respect to distance (df/dD). I was hoping the differentiation would be a bit complicated but it's just the power rule since I got a quadratic.

I am now trying to use related rates to find another rate of change, but I can't think of one that would be relevant. I was thinking of doing something with the volume of air required in relation to the distance to the first hole: dV/dD = dV/df x df/dD

However, this would be way too simple.

The variables I could change include length of the tube, volume of air, embouchure size, air speed and lung capacity.

If anyone can suggest a way to salvage this idea, I would appreciate it. If I can't find a way to make this work I will probably cry myself to sleep because it's the only semi-good idea I've had.

##### Share on other sites

You can also find df/dL, changes in pitch with respect to length of entire flute, instead of distance to first hole. In wind instruments, you tune by pushing in or pulling out a part of your instrument. You can also have data where you use different notes to tune, and see which one is better. Air speed and other quantities are not easily measurable. Remember to warm up your instrument each time so the temperature of air is constant and consistent between measurements.

## Create an account

Register a new account