Adding dB

Adding dB can be a challenge because dB, particularly when dealing with the world of acoustics, is based on the formula dB = 10 log10 (R), where (R) is a ratio between two powers or two pressures.

It is important to note that dB IL (intensity level) and dB SPL (sound pressure level) are equivalent, i.e., 20 dB IL ~ 20 dB SPL. It is only the reference values and units that differ. The reference for dB SPL is: .00002 Pascals (20 µPa) or .00002 Newtons/M2 (20µ Nt/m2); whereas the reference for sound intensity or power is 1 x 10-12 Watts/m2 or 1 x 10-16 Watts/cm2.

The following two formulae help us solve for dB:

dB SPL = 20 log10 (Po/Pr) where Po is the pressure being measured and Pr is the reference pressure.

dB IL is 10 log10 (Io/Ir) where Io is the power or intensity measured and Ir is the power/intensity reference.

Let’s say that I have two sources; one is 10 dB and the other is 15 dB and I want to know how many dB will result if the two sources are combined. Because the dB is not linear we know that adding of these two values will not result in a total of 25 dB, but rather in some lesser value.

The easy approach is to use a table or chart. Why go the easy route when we can figure it out for ourselves? It is important to understand the reasoning and the mechanism (procedure) behind the resultant dB value.

We have to break down the two sound sources into their basic components. By this I mean that we need to work backwards from what we know.

We know that 15 dB = 10 log10 (an unknown ratio we will call R); so how do we find out what (R) is? Well, I’m glad you asked J

We have to follow this formula:

dB = 10 log10 (R) can also be written (R) = antilog10 * (dB/10)

Note that we are dividing both sides of the equation by 10 in order to solve for (R).  Before we go any further, let’s define antilog.

According to Wikipedia ( ) “the antilogarithm function antilogb(y) is the inverse function of the logarithm function logb(x).”

The formula is: Antilog of x is = 10x


We  know that the log10 of 100 is 2  which can also be written 102 or 10 x 10  all of which equal 100.  The exponent of 100 is 2; therefore a log and an exponent are the same thing; the antilog of 2 (also known as x in the formula above) is 102 or 100.

Now we are getting somewhere. So, R is some unknown ratio of two powers or pressures. We need to know the R for 10 dB and the R for 15 dB. Using our handy dandy formula we are going to solve for both ratios.

(R) = antilog10 (dB/10)

(R) = antilog10 (1.5)

(R) = 31.62

To prove this let’s plug in our familiar formula for calculating dB

dB = 10 log10 (31.62)

dB = 10 * 1.49 (rounded off is 1.5)

dB = 15

So all we need to do now is figure out the ratio that results in 10 dB.

(R) = antilog (10dB/10)

(R) = antilog of 1

(R) = 10 (you already knew this because the log of 10 is 1!)

All we have left to do is add the two ratios to come up with a new ratio and plug it into our trusty dB formula and voila you have zee new value which is zee sum of zee original two sources.

dB = 10 log10 (R)

dB = 10 log10 (10+31.62)

dB = 10 log10 (41.62)

dB = 10 x 1.62

dB = 16.2

Conclusion: When you add 15 dB and 10 dB together you get 16.2 dB.

Wait a minute here—the formula for pressure is dB SPL = 20 log10 (R), but I said earlier that 20 dB IL ~ 20 dB SPL. So how can this approach work?

Let’s plug in some numbers and see what happens.

dB SPL = 20 log10 (R) and can also be written (R) = antilog10 (15 dB/20), therefore:

(R) = antilog10 0.75

(R) = 5.62

dB SPL = 20 log10 (5.62)

dB SPL = 20 * 0.749

dB SPL = 14.98 (rounded to the nearest decibel is 15!)

So whether you are using dB IL or dB SPL you still come up with the same answer. Remember we are dealing with ratios and that intensity is proportional to pressure squared and pressured squared is equal to the square root of intensity.

(I ∝ P2) or (P2∝√I)

Traumatic Brain Injury Conference

I have been working for the past few months in organizing a conference entitled “Traumatic Brain Injury: The Silent Epidemic.” This will be hosted by the Department of Communicative Disorders and Deaf Education at Utah State University on March 27th at the Eccles Conference Center on campus. It will be an all day conference and will be presented by an interdisciplinary faculty of experts who will address issues relating to TBI from the viewpoint of speech language pathologists, audiologists, lawyers, veterans vocational rehabilitationists, neuropsychologists, physiatrists, first responders, and TBI victims.

For further information go to

Early registration (before March 14th) is $75 and $25 for university students. Lunch is included. Parking is free.

This is a very timely event. Proceeds will support the Utah State University Student Academy of Audiology international hearing healthcare humanitarian mission.

Otoscopy (visual inspection of the outer ear)

One of the first skills acquired by audiologists is that of inspecting the outer ear (otoscopy). Otoscopy involves using a handheld light (freestanding or wall mounted) especially designed to enable the clinician to see the ear canal and the tympanic membrane. There is a light source and the end of the scope that allows for a mountable tip that helps focus the light into the narrow canal. These tips are known as specula and can be disposable or can be disinfected and reused. Audiologists are not the only ones who use this skill in assessing hearing. Hearing instrument specialists, pediatricians, general practitioners and ear nose and throat specialists are also trained in the use of the otoscope. One of  the techniques that we stress when teaching audiology students is the necessity of bracing when performing otoscopy. Bracing is the technique whereby the clinician, while inspecting the outer ear, uses the little finger of the hand holding the otoscope, placed against the patient’s head in order to avoid damage to the ear canal should the patient suddenly move.  It is very disheartening to see that many of the commercials on TV or even TV programs show otoscopy being performed WITHOUT the requisite bracing. Bracing will protect not only the patient from possible lacerations or abrasions of the outer ear canal, but also protect the clinician from possible litigation.

Investigative Audiology

Investigative Audiology is synonymous with Forensic Audiology. This is a very intriguing and relatively new area for the field of audiology. Expert witnesses and subject matter experts have been around for a long time particularly in the medical profession. Audiology really came into being since World War II, which means it is relatively young as an allied health profession. Many of the cases where an investigative audiologist has been involved as an expert witness have been cases where there is a worker’s compensation claim such as in mining and railroad. I have been involved in cases where my role was to determine if a practicing audiologist had caused injury to a patient. In one such case I was able to reconstruct the event leading to the injury of a patient by going on site to the clinic where the alleged injury occurred. Another case involved a law enforcement agency that had raided the wrong house and as a result there were alleged hearing related injuries. In this particular case in addition to reading depositions and affidavits I was also invited to examine the plaintiffs by evaluating their hearing in my clinic. Although there was some hearing loss, it was obvious that the loss had been exaggerated.  Another case involved the action taken by a physician while treating a patient that resulted in a hearing loss. I will soon be involved in evaluating a victim of a motor vehicle accident where there is evidence of mild traumatic brain injury (mTBI).  It is likely that in this case our clinic will need to evaluate hearing, as well as balance.

I have been asked how one gets into investigative audiology.  I really did nothing actively to alert law firms of my training or expertise. So I fell into this field quite by accident. One firm just did a Google search under forensic audiology in my state and my name popped up at the top of the list. Hopefully if I do my work to the satisfaction of those who have sought me out, the word will get out to others. I have formed a limited liability corporation (LLC) in consultation with a local law firm and a certified public accountant.  Recently I opened a website. Blogging seems to attract attention. I may eventually use one of the online services that provide directories of subject matter experts. I would like to expand this practice.

This is a great time to be an audiologist. The forecast for the next 30-40 years is that there will be a need for audiologists as the baby-boomers are hitting retirement age, are living longer than earlier generations, and will need hearing and balance related services.

Quarter Wave Length Resonator

The outer ear canal (external auditory meatus) is like a tube closed at one end. The length of the ear canal is roughly 2.3 cm. The fundamental resonant frequency is the lowest frequency possible with this configuration, i.e., only a quarter of the wave length can occur in that length of tube.

In order to calculate the hypothetical  resonance frequency (a.k.a. first natural mode) of a hard-walled tube closed at one end we must take the velocity divided by four times the length of the tube (in centimeters or inches). We have to do this to figure out the wavelength of one full cycle.

Therefore: the wavelength of an unknown frequency is 4 x 2.3 cm  = 9.2 cm

Velocity of sound = 34400 cm/sec

Resonant frequency = 34400 ⁄  9.2     = 3,739 Hz

The above is an idealized situation. One must remember that the walls of the external auditory meatus are not solid, and the meatus is not straight. The tympanic membrane is concave. All of these factors play a role in the resonance.

The actual resonant frequency of an average adult EAM is roughly 2700 Hz. Male resonant frequencies are usually lower that female resonances. Children resonant frequencies are higher still because of the shorter length of their EAM.

There is an advantage (boost) 12-17 dB in the amplitude of a signal at the resonant frequency. So if I were to put a small microphone in the ear canal connected to a sound level meter or other measuring device and then presented through an earphone a 70 dB level pure tone sweep through frequencies ranging from 125 Hz to 8,000 Hz, I would see an increase in the amplitude of the sound pressure level in the EAM the closer I got to 2700 where the response would peak. So the resonant frequency of the EAM is the result of a band pass filter centered at 2700 Hz. In other words, the physical characteristics of the tube closed at one end with a length of 2.3 cm allow frequencies closest to 2700 Hz to pass through while attenuating frequencies outside the band pass filter (above and below 2700 Hz).

So what?  What’s the take home message? Who really cares? Well, audiologists do because we need to take into account the acoustics of the ear canal when fitting individuals with amplification. The more we fill the EAM with an ear mold or custom hearing aid the more we alter the natural resonance of the canal. That in turn affects what gets through to the tympanic membrane and up the afferent auditory pathway.

Facial Nerve Disorders

One might not think that audiologists have much to do with the facial nerve (VII Cranial), but in fact they do. Anatomically the 7th nerve courses near the middle ear and in fact controls the little branch known as the stapedius muscle that attaches to the neck of the stapes (stirrup) which is located in the middle ear. Audiologists are trained in evaluating various systems via electrophysiology. One very specific approach to assessing facial nerve function is electroneurography (ENoG). The most common type of facial paralysis is Bell’s palsy. This may to be due to a virus; the etiology is actually unknown.  The prognosis in most cases is good. The onset of symptoms is 48-72 hours. Recovery can begin within a couple of weeks. Full recovery may take from 3-6 months.

Traumatic Brain Injury (II)

I have just spent several days attending an online course on traumatic brain injury (TBI) sponsored by the American Speech Language and Hearing Association. There were 13 presentations ranging from hearing loss and tinnitus to imbalance and dizziness in mild TBI patients, as well as the psychological and psychiatric implications, neuro-imaging such as CT scans and MRI and even newer technology with even greater resolution. Much of this information came from presenters working with veterans returning from deployment  in the Middle East. It is quite evident that there is a great deal of research going on in this area. This is a very complex issue. I believe that the key to successful treatment of victims and survivors of TBI is a dedicated team of professionals. This group would be comprised of health care providers  such as neurologist, social worker, occupational therapist, physical therapist, and speech language pathologist to name only a few, with a case manager (usually a physiatrist or neuropsychologist),  who will meet and staff each patient to ensure all the bases are covered and that proper referrals are made.

Otitis Media

Otitis media is an umbrella term that refers to inflammation of the middle ear. This condition is more common among children 0-8, with the highest occurrence during the first 5 years of life. This is not to say that older children, adolescents or adults are immune, however, the incidence in these last three age groups is minimal. One reason is that the Eustachian tube is almost horizontal in the newborn and infant and young child, but is much more vertical in the teenager and adult population. The Eustachian tubes (there are two of them) when functioning properly, help equalize the air pressure in the middle ear so that it is the same as atmospheric pressure in the outer ear canal. When the Eustachian tubes malfunction the result is an absorption of the oxygen in the middle ear by mucosal cells that line the cavity. In return for the oxygen the cells exude fluid. The longer the Eustachian tube malfunctions, the greater the accumulation of fluid in the middle ear.If the fluid is clear or honey colored, it is called serous otitis media. If the fluid is creamy or mild colored it is likely due to a build up of pus (by product of bacterial growth. This latter condition, if not treated can result in a great deal of pain for the patient and in the worst case scenario cause a perforation of the tympanic membrane. Treatment is usually antibiotcs. IF the tympanic membrane is bulging, an ENT can remedy the situation and immediately relieve the pain by a simple outpatient procedure known as a myringotomy.

Fortunately today ENTs and audiologists can recognize otitis media through visual inspection of the outer ear and tympanic membrane using a procedure called otoscopy. This is a simple examination using a small lighted (usually hand-held) scope with a magnifying lens through which the clinician inspects the ear drum and other landmarks. Another test that can assist in the diagnosis is called tympanometry, which be discussed later.