The Physical Theory
dB is the scientific symbol for Decibel
[A] unit of measurement used to express the ratio of one value of a power or field quantity to another, on a logarithmic scale.
The decibel is commonly used in acoustics as a unit of sound pressure level.
Well, that doesn't sound useful at first... but it helps us understand a few things.
Since dB are measured on a logarithmic scale, the sound pressure level at 120dB is 10 times higher than at 119 dB and 100 times higher than at 110 dB.
The human perception of the intensity of sound and light approximates the logarithm of intensity rather than a linear relationship (Weber–Fechner law), making the dB scale a useful measure.
That means that we humans don't perceive 120 dB as 100 times louder than 110 dB. We do notice a difference in loudness, but our perception of sound is closer to the logarithmic scale than to a linear scale.
The human ear has a large dynamic range in sound reception. The ratio of the sound intensity that causes permanent damage during short exposure to that of the quietest sound that the ear can hear is greater than or equal to 1 trillion (1012). Such large measurement ranges are conveniently expressed in logarithmic scale: the base-10 logarithm of 1012 is 12, which is expressed as a sound pressure level of 120 dB re 20 μPa.
As stated above, human perception of sound "approximates" the logarithmic scale of dB, but isn't equal to it. At the same sound pressure, high pitches seem louder to us than low pitches. To factor in this deviation in perception, different weightings can be applied to adapt the purely physical measurement of sound pressure level to our human perception.
Most commonly used is the A-weighting, which is expressed in a unit of dB(A) or often shortened to dBA.
[...] A-weighting, though originally intended only for the measurement of low-level sounds (around 40 phon), is now commonly used for the measurement of environmental noise and industrial noise, as well as when assessing potential hearing damage and other noise health effects at all sound levels; indeed, the use of A-frequency-weighting is now mandated for all these measurements, because decades of field experience have shown a very good correlation with occupational deafness in the frequency range of human speech.
This deviation in loudness perception is caused by many different factors, like the form of our outer and inner ears, the sensitivity of different neurons to different frequencies and the age of the listener (we have a tendency to lose the ability to perceive high frequencies throughout our whole lives).
There are several other weighting curves, but A and C frequency-weighting are the most common.
Obviously, dogs perceive sounds at a different level than humans, so the measurements in dBA cannot be applied to dogs. But since dogs cannot answer questions like "How loud is this noise?" there is no separate weighting curve for dogs.
The 1992 study Auditory Perception shows the following audiograms for the perception threshold of sounds in dogs on page 167:
The dotted line is the hearing threshold of humans (for comparison). The lower the line, the better the test subject could perceive sounds. The line of the dog (middle) is shifted to the right, which tells us that dogs hear higher frequencies better than humans, but lower frequencies worse than humans.
That means that a dog horn with a high pitch (comparable to a whistle) seems even louder to dogs than to humans. On the other hand, a deep sound like a car engine probably seems less loud to a dog than a human.
Danger of hearing loss
Here it gets complicated. Many tests have been conducted for decades to determine the auditory threshold of dogs (how quiet a sound they can detect), but it's harder to determine how loud of a sound causes a dog pain or hearing loss.
I found an interesting fact in the book "The Behavioural Biology of Dogs":
In the middle ear, two of the smallest muscles of the body are situated: one of them is connected with the stapes and the other one with the tympanic membrane. The contraction of these muscles decreases the transfer of vibration through the middle ear. A reflex elicits the contraction when the incoming energy of the sound is too high. This reflex is also activated immediately before a dog starts to bark and therefore offers protection to its own ear.
So the sound energy of the barking of a dog warrants a protection inside the dog's own ear.
A listing in cuteness.com compares the barking of dogs with different everyday sounds:
[A] sewing machine is around 60 decibels -- the same loudness as a "starting point" bark. A child in the midst of a shrieking tantrum goes to around 110 decibels, which is the same as dog barks on the noisier end of the spectrum.
And on Quora you can find the following claim:
The loudest dog in the world, as of 2013, had a bark that was 113.1 decibels. Most dogs bark between 80 and 90 decibels in volume, about as loud as a shouting human.
All things considered, I guess you can safely compare the effect of such a horn on a dog's ear to a human ear:
- It will cause pain to the dog
- It will cause temporary hearing loss after very short exposure (a few seconds)
- It will cause permanent hearing loss after short exposure (more than 2 minutes)
If you want to measure the actual loudness of this horn, don't forget to wear hearing protection yourself.
I have no experience with the effectiveness of such a dog horn against attacking dogs. I presume it emulates a really loud bark to deter the attacker.
As an emergency measure it should not cause any permanent damage or hearing loss.