I was asked a question recently about the fabled Walls of Jericho that came tumbling down in biblical times. This person wanted to know the acoustics of such an event and whether it could have actually happened. After all, we know the acoustics of soprano singers being able to break high quality crystal glasses.
The short answer is “no- this could not happen”.
The long answer involves the acoustics of quarter wavelength resonators, ram’s horns, and the very heavy stones built into the Walls of Jericho.
The Walls of Jericho:
Starting with the walls of Jericho or, for that matter, any stable structure using the building materials available back then, the resonant or best vibrating frequency would be less than 1 Hz and most likely even less than 0.1 Hz. In order to set the Walls of Jericho in vibration enough to break the mortar or other joining materials, one would need a sufficiently intense low frequency stimulus on the order of 1 or 0.1 Hz or 0.1 vibrations per second.
This same line of reasoning holds true for breaking a high quality crystal glass; in this case, the resonant frequency may be 3000-4000 Hz because the glass is so brittle. A well-trained and well situated soprano may indeed be able to generate a sufficient sound level at these higher frequencies to be near the resonant frequency of the crystal. But thick and heavy walls are not fine crystal; thick stone walls have resonant frequencies that are much lower.
What about many men yelling at the Walls of Jericho?
Let’s deal with the vocal tract first. If I recall my religious studies class, there were many men and blowing the ram’s horn, and ostensibly these two noise sources could be sufficient to knock down the thick stone walls of the city of Jericho.
The human vocal tract is roughly 17 cm long and extends from the vocal chords to the lips (with a nasal cavity in parallel to the oral cavity). For the vowel [a] as in ‘father’ which these men undoubtedly were yelling (rather than an [s] which would have been annoying, but not all that loud), the first mode of resonance (or first formant) would be 500 Hz. The math behind this is based on the formula F=v/4L where v is the speed of sound and L is the length of the resonating chamber. Assuming that the speed of sound in the hot (but near sea level) city of Jericho was 34,000 cm/s, and the vocal tract length was indeed 17 cm, the resonant frequency would be 34,000/4 x 17 = 500 Hz…. I love it when calculations work out to such perfectly rounded numbers!
In the human vocal tract we can get sounds with lower resonant frequencies than 500 Hz (for the first formant or F1). These are the high vowels ([i] and [u]). These are “Helmholtz” resonances and the calculations would indicate resonances of 125 Hz – still far above the needed 1 Hz or 0.1 Hz needed to cause sufficient stone wall vibration.
Couple these resonances with the fact that very few people (with the exception of large truckers and football linebackers) have fundamental frequencies (f0) of their voices at less than 100 Hz and one can say that the lowest possible frequency emanating from a person’s vocal tract is above 100 Hz (and most likely higher than 125 Hz). Note: I checked the biblical census and there were no big giant truckers or football players back then.
But even if these attacking men were all large truckers (perhaps from a visiting transportation crazed nation), the lowest frequency that could be yelled would be on the order of 100 Hz. This would be between 100 and 1000 times higher than what would be necessary to be sufficient to vibrate and potentially destroy the Walls of Jericho.
Even a million men simultaneously shouting would have no vocal energy below 100 Hz. (After all, 1 million x 0 is still 0).
I think that would be sufficient to dispel the myth that thousands of voices would be needed to destroy the Walls.
What about the ram’s horns and the Walls of Jericho?
Well, being from a city, I haven’t run in to too many rams lately, but I have visited my share of zoos and do have access to the internet. Rams have horns that are on the order of 15-20 cm (6-8” in the old American units). Assuming that the ram’s horn functions like a quarter wavelength resonator (like a trumpet or our vocal tract during the articulation of [a]) we can do the same calculation as above; namely F= v/4L or 34,000 cm/s / 4 x 20 cm = 425 Hz… again a round number… a coincidence??
If the lowest frequency that can be generated by a ram’s horn is 425 Hz, it would be impossible to generate a frequency of 0.1 Hz or 1 Hz necessary to vibrate the Walls of Jericho. And like the thousands of men, you could have 1 million ram’s horns blowing at once, and there would still be no energy at 1 Hz or even below 425 Hz to vibrate the Walls.
And the picture of the ram’s horn looks as if it’s almost half a meter long … must have belonged to the fabled “elephant ram”! Even if the ram’s horn was 4 times as long as the one used in the above calculations (i.e., 80 cm or about 2.5 feet), the lowest possible resonant frequency would still be well above 100 Hz, so even that could not have caused the Walls of Jericho to shake and fall.
In order for a ram’s horn to generate a 1 Hz resonant signal, the quarter wavelength resonator formula (F=v/4L) tells us that a ram’s horn would have to be 8250 cm long which is 82.5 meters or 271 feet!
And like getting the caramel in the Caramilk chocolate bar….it’s Science!
AND I have figured out how they did get the caramel in the Caramilk chocolate bar!