How To Hear Acceleration Without Modern Technology?

In our modern technological world, we have all sorts of solutions to help us measure acceleration. But what if you lost access to all of modern technology? How would you measure acceleration then?

This is essentially the conundrum that Italian polymath, Galileo Galilei faced in the 17-th century. He found himself in a situation where he had to measure acceleration caused due to gravity on free-falling objects.

In this article, I start with the background story that led Galileo to this point (he apparently preferred being called by his given name). Then, I present his brilliant resourcefulness and smart inventions that led him to solve this problem. Finally, I discuss what you and I could learn from this ingenious technical feat.

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The Background Story — Aristotle and Strato

Way back in ancient Greece (4th century B.C.), Aristotle asserted that the speed of a free-falling body was proportional to its weight and inversely proportional to the density of the medium it was falling through. He mentioned that there was some sort of acceleration involved, but did not go deep into the topic.

A few decades after Aristotle, Strato questioned the notion of constant speed (given the same weight) for free-falling bodies. He pointed out that a stone dropped from a greater height caused a greater impact on the ground than when it was dropped from a lower height. This suggested that there was some sort of acceleration involved.

Thousands of years later, in the 17-th century A.D., Galileo took interest in this topic and wished to right what he saw was going wrong in science.

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Misconceptions of the Time and Galileo’s Solution

Until this point in the 16-th/17-th century, people of science had not challenged the notion of acceleration because it was hard to detect by sight. Most scholars turned to some form of slowed-down falling motion like an object sinking in water to understand the phenomenon. They observed that there was some initial acceleration followed by constant drop-speed. So, the notion went largely unchallenged.

By this time, Galileo had already disproved Aristotle’s notion that free-fall speed was proportional to weight. In one of his books, he documented that a very heavy ball and a lighter ball would roughly land at the same time on the ground when dropped from the tower of Pisa. He noted that for very light objects, air resistance would play a role in slowing the fall down, but when air resistance (friction, in general) becomes negligible, the speed should be the same.

Here is an experiment conducted as part of Apollo 15 to prove Galileo’s findings:

Galileo figured that he had to somehow slow down the effect of gravity enough to understand what was going on. But at the same time, he would need to be careful enough not to affect the free-fall mechanic as water does.

The Acceleration Hypothesis

Galileo hypothesized that a falling body accelerates uniformly. That is, it gains an equal amount of speed in equal intervals of time. If a body falls from rest, it would move twice as fast after two seconds as it would have moved after one second. Similarly, after three seconds, the body would be falling at three times the speed as it would have after one second.

Armed with this hypothesis and knowledge of friction caused by water, Galileo knew that he had to come up with a practical experiment. Ideally, he would need to slow down the effect of gravity without changing the free-fall mechanic of the falling body.

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Slowing Down Gravity Effects

Galileo eventually came up with an ingenious idea. He designed a ramp that was about 5.5 metres long, about 0.2 metres wide, and three finger-breadths thick (which appears to be a measuring convention back then).

On its edge, he cut a channel that was about one finger in breadth. He went on to polish it and smoothen it nicely. He then lined it with a parchment that was also as polished and as smooth as possible.

The ramp was then sloped at a height of 0.5–1 metres at its highest end. Finally, he took a hard, smooth, and “very” round bronze ball and rolled it down the groove.

Of course, all of this did not happen instantaneously. He carefully experimented with heights, angles, and different objects to narrow down on this setup. He experimentally verified and slowed down the effects of gravity optimally enough for him to measure acceleration. At the same time, the slope was just shallow enough for wind resistance to cause a negligible effect on the phenomenon. He also ensured that the ball-ramp friction did not change the free-fall acceleration ratio significantly.

Measuring Acceleration

After establishing this setup, Galileo rolled the ball down the ramp. First, he rolled the ball along the full length of the ramp. Then he also rolled it along partial lengths of the ramp, such as three-fourths, half, and quarter. Each time, the time taken for the ball to start and exit the ramp was recorded. And he repeated each of these experiments hundreds of times until the deviations in measurements were not greater than “one-tenth of a pulse-beat”.

Measuring Time

In order to measure time accurately, Galileo used a water clock. He placed a large vessel of water at an elevated position and soldered a pipe of small diameter to its bottom. This enabled a thin jet of water to flow out at the end of the pipe. Galileo then collected the water at its outlet in a glass container. After each experiment, the water was weighed. The difference in weights and the ratios between weights when the ball was rolled full length as compared to partial lengths gave Galileo an understanding of acceleration.

The Results

Galileo noted that the ball gained speed the longer it rolled. If the ball took 1 unit of time to roll down quarter-length of the ramp, then it took just 2 units of time to roll down the entire ramp. Based on this, Galileo deduced that there is uniform acceleration taking place. That is, for each unit of time, there is an equal increment of speed. In much simpler terms, if the speed of the rolling ball is 0 at the start, then the speed increases to 1 unit after 1 unit of time, to 2 units after 2 units of time, to 3 units after 3 units of time, and so on.

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How To Hear Acceleration?

Since acceleration due to gravity is hard to detect by sight, Galileo came up with the creative proposition that one could hear acceleration! He used the same ramp/ball setup and arranged bells on the ball’s path on its way down the ramp. This way, one could hear the bells ringing as the ball went past.

When the bells were equally spaced across the ramp, one could hear the tones getting faster and faster. Using the data Galileo had collected from the water-clock experiment, he then moved the bells and played around with their positioning.

Eventually, when he placed the bells as per the ratios (where the distance between any two bells is increased exponentially as one moves down the ramp), the bell tones were uniformly distributed. Imagine that the slope is 8 metres long. Then when the bells are placed at 1, 2, 4, and 8 metres respectively, the bell tones would be uniform.

Galileo experimented with the positioning of the bells to narrow down on the value of acceleration due to gravity. Through this process, he established that acceleration was related to the square of the distance.

What Does This Mean for You and Me?

In our modern technological society, we have access to all sorts of high-end solutions even to our most fundamental problems. Almost everything is computerized and data-driven.

As young school students aspire to become valuable contributors to society, mastering technological skills relevant to our current society has taken priority.

However, there is an argument that states that resourcefulness is becoming scarce when it comes to innovation and problem-solving.

Resourcefulness here would mean achieving more with less. This argument could be extrapolated to more climate-friendly solutions, more humanistic technology, etc.

The story of how Galileo attacked such complicated problems with such little resources is an inspiration for all of us to focus on ground fundamentals.

We stand to gain from attacking problems at a fundamental conceptual level first before turning to computers or automated/recipe-based solutions.

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Further reading that might interest you: Logarithms: The Long Forgotten Story Of Scientific Progress and  The Thrilling Story Of Calculus.