Physics of the Ear

The ear system

We can divide the ear into three parts, these parts are defined by their position and functions and are known as, the outer ear (the part visible to us), the middle ear which is the apparatus that focus and transforms the vibrations, and the inner ear that connects our system to the nerves and brain.

The outer ear

The outer ear is the visible part. It is made up of the pinna, the ear canal that ends where the middle ear begins, at the outer part of the tympanic membrane. The pinna is shaped to catch the sound from the front and has ridges to direct it towards the tympanic membrane. This structure helped to focus on the sounds emitted by a prey.

Middle ear

The middle ear is where the sound is transformed from a pressure wave to an electric signal. In this section, three small bones act as mechanical transmitters of the sound, they are called: the malleus, incus, and stapes. This is an important function because it acts as an impedance adapter, allowing the ear to have an extensive amplitude range of perception with the lower limit of 20μPa being absolute silence. As a comparison, around 60μPa is the sound pressure of normal breathing.

Two thresholds determine the upper limit of our hearing range, the first is where we start to feel pain, and the second is where the intensity of the sound causes harm to the ear.

Inner ear

This part of the ear is hidden from sight, enclosed in a bony labyrinth where the cochlea, semicircular canals and the vestibule are located. When it arrives here, the sound has been attenuated by the middle ear and is ready to be analyzed, transformed and transmitted to the brain, where it will be processed.

Physics of the Ear: Measuring pressure and sound

Our ears are very sophisticated instruments with incredible sensitivity. We can carry out calculations on this range of perception.

Physics of the Ear: From air pressure to decibels

Sound waves are pressure waves, which means that information travels thanks to the alternation of rarefaction and concentration zones of particles in the air.

We measure pressure in pascals. Our hearing covers a range from a millionth of a pascal to hundreds of pascals, and sometimes we need to describe even louder sounds. It isn't convenient to use this unit, so we apply a logarithmic scale to this quantity to reduce the excursion range from millions. The decibel is an intensity scale and is used to represent a sound's pressure level; this is defined with respect to a reference that is the softest sound we can hear. For definition:

\[L_p = 20 \space \log(\frac{p}{p_0}), \space P_0 = 20 \space \mu P_a\]

Where Lp is the pressure level relative to the pressure p, and p₀ is the reference pressure. Let's take an example: we want to know the pressure level corresponding to 20 Pa:

\(p = 20 \space P_a\)

\(L_p = ?\)

\(L_p = 20 \space \log(\frac{p}{p_0}) = 20 \space \log (\frac{20}{20 \cdot 10^{-6}}) = 20 \log 10^6 = 120 dB\)

We say that 20Pa corresponds to 120dB SPL. SPL stands for sound pressure level to indicate we're talking about sound since the logarithmic scale has many uses.

Figure 3.- Decibel scale showing the noises we usually hear and their normal range. It also shows the sensations we have for every scale, Camacho - Study Smart Originals

The same evolutionary processes that shape the human hearing system are the ones that constrain the range of frequencies we can capture. The range of sound we can hear is the result of this process.

Consequences of damage to the ear

The ear is a complex, delicate system, even though it is very adaptive. As with every other part of the body, it can be subject to damage. Here are some potential consequences.

Physics of the Ear: Loss of hearing

The most common issue is the loss of hearing. This happens naturally with age - a child has a spectrum of hearing that goes from 20Hz to 20KHz, while an adult won't hear sounds above approximately 15KHz. Human hearing is limited by its physical characteristics (you won't be able to hear any sound too low to cause vibrations in your ear) but also by evolution as most of the human senses work in the range that is useful for us to receive and analyze information.

After aging, loud sounds are the leading cause of hearing loss. These can cause damage instantly or are partially harmful, leading to more severe damage with exposure over time. The threshold of pain begins at 130dB. Damage occurs immediately when the sound pressure is 140dB or more. For instance, it takes just one rifle shot to cause a gap in hearing of around 5KHz. Hunters often experience this.

Another malfunction of hearing is tinnitus. This is described as hearing sounds such as ringing or hissing where there is no cause for the sound. Tinnitus can be caused by exposure to loud noises.

Physics of the Ear: Balance

The inner ear is responsible for another important function: balance. We have three semicircular canals that perceive movement from the three dimensions of space, while otoliths are structures that detect linear acceleration. A well-known malfunction of the vestibular system is vertigo. This is defined as the perception of movement when there's none.