# Designing a siren to vary pitch with port width/pattern. Advice needed

• Background: I am trying to design a multi-pitch port siren with one central shaft at 3300 rpm. I've calculated the number of ports needed for each frequency to be n = f(60/rpm). This approach gives me fractional n for many values, which I want to remedy. I am not super knowledgeable about waves, I am just learning them in university.

• Question: I am curious about the effect of changing port/hole width on the sound produced. I know pitch is dependent on frequency, but if the width of each hole was shortened what effect might that have on the pitch/tone? Would an elongated 'trough' or 'crest' (forgive me I don't know what the term would be for this) effect the pitch at all? Another idea I had was to create an irregular hole pattern, and then maybe the resulting frequency would be some kind of average between the periods between the holes? Any other ideas for modifying frequency with a set number of holes? Thanks in advance. pic for reference

• Seen real ones that look like this - have you researched them? Feb 27 at 8:18
• That's an interesting question. My first thought was that the port width might affect the harmonics of the fundamental and that tone would change. Two seconds later I thought, "But the harmonics have to be integer multiples of the fundamental so how would that relate to the infinitely variable port width?" Five minutes later and I haven't got past that! Feb 27 at 9:29
• In relation to the musicality of the tones generated, the simplest ratios give the most pleasing result. 1:1 = unison. 2:1 = one octave. 3:2 = perfect fifth. 4:3 = fourth. 5:4 = major third. 6;5 = minor third. Good 'ol Pythag did a load of work on this. More here: en.wikipedia.org/wiki/…. Feb 27 at 9:38

## 1 Answer

A siren works by suddenly opening a valve (one of the ports) and allowing a burst of air to escape, then closing that valve. for slow openings and closings that burst represents a square wave pressure pulse with a width determined by the duration of the opening and the rotating speed of the valve disc or cylinder.

That square wave is rich in higher harmonics, which you can actually hear when the siren is running very slowly.

Since the air being flung out the opening possess mass, it takes time to accelerate to full speed and thus the square wave pressure pulse has its sharp edges smoothed off, which suppresses the higher harmonics at higher speeds.

As we increase the siren speed or make the openings narrower there then comes a point where the valve is not open long enough for the escaping air to reach full speed before it closes again and the pressure pulse starts looking more like a sine wave than a square wave. So the timbre will depend on the siren speed.

The problem of generating noninteger frequency notes is solved by constructing a second siren that is geared to run at a different speed than the first one. In this way you can generate all the sharps and flats needed to play a complete scale by switching between the two sirens.

This principle is used in the Hammond Organ (google it) to electromechanically generate musical scales with all sharps and flats.

• So you are suggesting I create different sirens with the 'integer' frequency tones to get all the notes I desire. Thank you for the suggestion, I will look up the hammond organ. I am still curious what would happen if you had a varied spacing between the ports for one note, if you have any insight into this. Thanks! Feb 28 at 17:18