Back in 2009 I received a philosophical question, something not too different from “How many angels can dance on the head of a pin?” It’s about how many people could hear the voice of Jesus at one time. Below I show the actual question followed by Section 1 of my answer. Here I idealized the physical listening conditions so that I could establish the maximum possible number of listeners. In later sections, which I will soon publish, I work towards more practical answers.
“I was discussing the following question with some colleagues and was wondering if you can help (I saw some of your online articles which led me to believe that you are an expert in the matter):
Given the most optimal acoustic conditions and the loudest human voice, how many people can hear the voice of a person with no microphones or speakers?
Would this depend if the setup was inside or outside?
Can you give a rough estimate of how many people could hear inside and how many can hear outside?
I am assuming the best conditions, i.e. the perfectly designed auditorium or concert hall, on a mountain or in a valley,…
If outside, how much can the weather conditions effect matters – (i.e. humidity, rain,…) ? ”
Professor Elie Feder
Dept. of Mathematics
Kingsborough Community College- CUNY
The question has been asked, “How many people could Jesus address at once?” Utilizing acoustic engineering principles and excluding the possibility of a miracle, we can determine the maximum number of people who could physically hear Jesus by the following “ideal listening tube” analysis.
If a raised voice, intending to communicate to many, produces a sound level of 85 dB,A at 1.5’ and if everyone listening was to receive a portion of that sound, at a level of 45 dB,A in each ear, what is the maximum number of people who could receive their portion of that physical, unamplified sound?
If we let his sound wave expand to a sound level of 45 dB,A and then assign each ¼ square inch of that wavefront to each ear of each listener, we can determine how many possible listeners there could be. Physically we can imagine that Jesus is speaking and at some distance away is a large grid in a spherical shape. A pair of listening tubes is plugged into each opening of the grid, as close to each other as possible. Each pair of ideal lossless listening tubes extends out to each listening person.
The distance from Jesus to where the sound level drops to 45 dB,A is the radius of that sphere calculated by r = 1.5’ x 10^((85-45)/20) = 150’. The area of a sphere is: A = 4 x pi x r^2 and for this sphere it becomes: A = 4 x pi x 150^2 = 282,600 sqft.
If one ear gets a sound duct that is ¼ inch square, there are 4 x 4 = 16 of such ¼” square sound ducts per square inch or 8 pairs of listening ducts per square inch. Since there are 144 sqin in one sqft we have 144 x 8 = 1152 people plugged in and listening per sqft of the listening sphere grid. We have 282,600 sqft at a sound level of 45 dB,A occupied by sound ducts for 1152 people per sqft. This arrangement has the potential to deliver audible sound to 325 million people.
According to the world population growth scale we see the world population leveling off at about 170 million people between 500 BC and 500 AD which is when Jesus would have been speaking to the people. This means the voice of Jesus had enough sound power that it could have been directly piped to twice the number of people alive at that time in history.
If Jesus wanted to physically speak today with the world population at 7 billion, he could physically address one out of every 20 people alive today through listening tubes.