Kerry Parker-Price of Wellington asks :-

How do steam train whistles get that woo-woo sound?

John Campbell, a physicist at the University of Canterbury responded.

The fact that I am responding means that we dont know. My acoustics expert at Cambridge, England, didn't know of any studies and suggested it would make an excellent undergraduate project. Possibly the last person to write on the topic was Lord Rayleigh over a hundred years ago. So all I can do is refer to general principles.

Whistles and many musical instruments (eg organs) use resonance of a fixed cavity. Some musical instruments, eg the trombone, allow for the cavity length to be changed thereby altering the resonant frequency. Steam whistles have the great advantage that they have no moving parts, apart from the valve that lets steam in.

A fixed cavity, such as an organ or bugle, resonates at frequencies which are governed by the length of the tube and the speed of sound in the gas it encloses. This limits it to a few notes; the fundamental frequency and its harmonics, ie the fundamental frequency multiplied by a series of small integers. A 303 rifle barrel can be played as a musical instrument, though, as an army bandsman said after playing the Post-horn Gallop, it is limited to three notes, four if you struggle.

A standard fixed cavity is one closed at one end. The air against the wall at the closed end cannot move. The air just outside the open end is also stationary in resonance. Just where this point is relative to the end of the tube depends on may things such as the air pressure used and the diameter of the tube.

Anything that changes the speed of sound in the cavity will alter the resonance frequency. The human windpipe is a cavity and the sound can be altered by changing the gas present. I often breath in helium gas, then talk like Donald Duck.

The steam whistle is more complicated in that steam is a mixture of air, water-vapour and water droplets. The speed of sound in air (about 330 metres per second) is quite different to the speed of sound in water (1410 metres per second). A mixture involving droplets is very complicated. Also the steam is hot so the cavity warms up and changes length slightly. The composition and temperature of the steam alters. Hence it is not surprising the speed of sound and the steam speed alter with time after the whistle is opened.

On the other hand a good steam train driver can manipulate the degree to which the valve is open thus altering the speed and properties of the input steam. Many drivers have their own signature.

It is often the simplest of physics that has the most complicated of behaviours.