Shaded by a canvas sheet from the heat of the sun, John Strutt watched the ancient pyramids pass by as his houseboat continued on its cruise up the Nile. As the days passed he had felt the aches in his joints ease and his vigour return. Now he felt strong enough to return to his cabin and start to develop his recent thoughts on mathematical theories of sound and vibration into a formal treatise.
In 1871 John William Strutt Lord Rayleigh had married Evelyn Balfour – the sister of Arthur James Balfour who went on to become Prime Minister of Britain 30 years later.
Unfortunately, just after the marriage, Rayleigh suffered a severe bout of Rheumatic fever and he was advised that a Nile cruise was the cure. So he and Evelyn set-off in late 1872 for Egypt.
The treatise that Rayleigh wrote on the cruise became his seminal work – ‘The Theory of Sound’. This set-out the fundamental equations describing the propagation of sound and vibration in 3 dimensional space and was a hugely comprehensive work published in 2 volumes and with over 1,000 pages in total.
“My endeavour has been to lay before the reader a connected exposition of the theory of sound” from the foreword to Rayleighs ‘The Theory of Sound’ 1877
Fast forward to 1984 and a young PhD student in Manchester, UK is studying how to reduce the noise emitted by submarines as they travel underwater. In submarines, machinery such as pumps, motors, and engines are located on large, thick steel plates (‘rafts’), which in turn are supported by carefully designed viscoelastic (rubbery) mounts. This significantly
reduces vibration transmitted to the hull.
However, an issue arises with the hydraulic hoses which run from the machinery rafts, often connecting to remote machinery such as steering gear. These hoses can become the main vibration transmission path to the hull. Due to their ‘springy’ nature, they have a number of resonant frequencies where they actually amplify the source vibration – if these frequencies correspond to, say, the running speed of the pump, then this gets transmitted to the hull and into the sea as a distinct sound – not desirable!
So my work (for I was the young researcher) was to create mathematical models to be able to forecast the resonant characteristics of the multitude of hoses. This involved many variables including the stiffness and damping of the hoses in 6 axes (orthogonal and rotational), the tension, pressure of the hose, its fixings etc. And as a basis for the mathematical models – it was all there in Rayleigh’s ‘Theory of Sound’
But the thing that I find most fascinating….. is that many of the models involved complicated sets of differential equations, that essentially can only be solved by numerical iteration. This means that whilst Rayleigh set out the models in great detail – they could never be solved or applied by him as the iterative methods required would take clerks working for centuries to do the maths.
Here, for the first time, over a hundred years later, I was applying these models and through the use of computers (still quite new in 1984!) was able to generate solutions in seconds to help design nuclear submarines.
I am still in awe at the vision, insight and sheer brain power that Rayleigh had. Working in the cabin of a houseboat on the Nile, he was able to develop the entire basis of the theory of Sound and Vibration, working from first principles with just paper and fountain pen.
And of course – my experimental work showed that all Rayleigh’s theories relating to my studies were correct and provided a good model of the behaviour of the hoses.