Changes

<strong>Step 17:</strong> If math equations give you the urge to throw up, you'll definitely want to skip this step. This step will explain how you can attempt to "tune" your train whistle to a certain pitch or chord. The train whistle will still sound good even if you pick random hole depths; you can even choose to make all the holes the same depth for a single tone too. Two pieces of advice... First, I wouldn't recommend drilling a hole that is within a half inch of the total length of the workpiece (in our case, that means don't drill a hole deeper than 9 inches) because you don't want to accidentally drill through the bottom. Secondly, I wouldn't recommend drilling a hole shorter than 3 inches. Holes this short require a very fast stream of air to resonate, and they may not work well alongside the other deeper holes. The general rule of thumb is that deeper holes require less air to resonate than shorter holes.

<strong>Step 17:</strong> If math equations give you the urge to throw up, you'll definitely want to skip this step. This step will explain how you can attempt to "tune" your train whistle to a certain pitch or chord. The train whistle will still sound good even if you pick random hole depths; you can even choose to make all the holes the same depth for a single tone too. Two pieces of advice... First, I wouldn't recommend drilling a hole that is within a half inch of the total length of the workpiece (in our case, that means don't drill a hole deeper than 9 inches) because you don't want to accidentally drill through the bottom. Secondly, I wouldn't recommend drilling a hole shorter than 3 inches. Holes this short require a very fast stream of air to resonate, and they may not work well alongside the other deeper holes. The general rule of thumb is that deeper holes require less air to resonate than shorter holes.

Most Western music uses the concert pitch standard of A4 = 440 Hz. It's called "A4" because it occurs in the 4th octave on a standard 88-key piano. It's the first "A" note above middle C. If we double the frequency of A4, we get A5 = 880 Hz which is exactly one octave above A4. Most music derives from the 12-note chromatic scale that divides the notes from the root note to the octave into 12 "even" values. This means that each note is related to its adjacent note (up or down) by a factor of the {{radic|''2''|12}} {{math|sqrt|''S''}}, {{radic|''S''|2}}, or S^1/2. You can see a table of notes with their respective frequencies at this link ([https://pages.mtu.edu/~suits/notefreqs.html Frequency of Musical Notes]). Ok, enough music theory... back to the train whistle. We are making an assumption that the acoustic resonance of the drilled holes in our train whistle functions like a tube with one end closed off (stopped pipe). The equation for the resonance of a stopped pipe is shown in the image below. The point is: the equation shows that you can change the frequency/pitch of the note based on how deep you drill the holes in your train whistle. The diameter (d) of our holes will be fixed to 1/2 inch because that's the longest drill bit we have. Though there are many factors that affect the speed of sound, we can approximate it with 13504 in/s. We will also set n=1 because we are only concerned with the fundamental frequency, not higher order harmonics. Keep in mind that our assumptions mean that this equation will not yield exact results. However, it is close enough for our purposes, and based on the prototype I built, I was able to add a constant value that makes the equation more accurate in this case (C = 3/8 inch). You are welcome to experiment with these equations to produce various notes/chords to your own peril. The recommended hole depths given below are intended to produce a G-major or a G-minor train whistle. Results may vary.

Most Western music uses the concert pitch standard of A4 = 440 Hz. It's called "A4" because it occurs in the 4th octave on a standard 88-key piano. It's the first "A" note above middle C. If we double the frequency of A4, we get A5 = 880 Hz which is exactly one octave above A4. Most music derives from the 12-note chromatic scale that divides the notes from the root note to the octave into 12 "even" values. This means that each note is related to its adjacent note (up or down) by a factor of the {{math|radic|''2''|12}} {{math|sqrt|''S''}}, {{radic|''S''|2}}, or S^1/2. You can see a table of notes with their respective frequencies at this link ([https://pages.mtu.edu/~suits/notefreqs.html Frequency of Musical Notes]). Ok, enough music theory... back to the train whistle. We are making an assumption that the acoustic resonance of the drilled holes in our train whistle functions like a tube with one end closed off (stopped pipe). The equation for the resonance of a stopped pipe is shown in the image below. The point is: the equation shows that you can change the frequency/pitch of the note based on how deep you drill the holes in your train whistle. The diameter (d) of our holes will be fixed to 1/2 inch because that's the longest drill bit we have. Though there are many factors that affect the speed of sound, we can approximate it with 13504 in/s. We will also set n=1 because we are only concerned with the fundamental frequency, not higher order harmonics. Keep in mind that our assumptions mean that this equation will not yield exact results. However, it is close enough for our purposes, and based on the prototype I built, I was able to add a constant value that makes the equation more accurate in this case (C = 3/8 inch). You are welcome to experiment with these equations to produce various notes/chords to your own peril. The recommended hole depths given below are intended to produce a G-major or a G-minor train whistle. Results may vary.

TW17

TW17