Physics of the ear (3.10.2)

The human ear is divided into three main regions: the outer ear, the middle ear, and the inner ear.

• Outer ear: Consists of the pinna, external auditory canal (ear canal), and tympanic membrane (eardrum). The pinna collects sound waves and directs them through the auditory canal toward the eardrum.

• Middle ear: Contains the ossicles (malleus, incus, stapes) and the eustachian tube. The ossicles amplify vibrations from the eardrum and transmit them to the oval window of the inner ear. The eustachian tube equalises air pressure between the middle ear and the atmosphere.

• Inner ear: This includes the oval window, the round window, the cochlea, and the semicircular canals. The cochlea converts mechanical vibrations into electrical nerve impulses sent to the brain via the auditory nerve, and the semicircular canals help maintain balance.

The outer ear captures and channels sound waves toward the eardrum. It includes the pinna, auditory canal, and tympanic membrane.

• The pinna gathers sound from the environment and directs it into the auditory canal (ear canal) via reflection. By focusing incident sound energy into a smaller area, the pinna increases the intensity of sounds.

• The auditory canal carries the focused sound waves to the eardrum and enhances sensitivity to sounds in the range to due to resonance effects. This belongs to the range of human hearing, spanning approximately from to

• The tympanic membrane (eardrum) vibrates in response to incident sound waves, converting pressure variations into mechanical vibrations. This marks the transition point between the outer and middle ear.

Together, these structures initiate hearing by collecting, amplifying and converting sound energy into mechanical energy.

The middle ear increases the strength of mechanical vibrations and transmits them to the inner ear. The middle ear contains the ossicles and the Eustachian tube.

• The ossicles are a bone structure that consists of three parts: the malleus (hammer), incus (anvil), and stapes (stirrup). Together, they form a lever system that boosts the force of vibrations in the eardrum by a factor of 1.5. They transmit vibrations from the eardrum to the oval window in the inner ear.
• These bones adjust their tightness to control sound transmission. They tighten in quiet settings for efficiency and loosen in loud environments to reduce damage risk.
• The Eustachian tube connects the middle ear to the throat, allowing air to enter or exit to balance pressure in the middle ear with the pressure outside.

The inner ear translates mechanical vibrations into nerve signals and helps with balance. It includes the cochlea, the oval window, the round window, and the semicircular canals. This part of the ear is responsible for both hearing and equilibrium.

• Vibrations from the ossicles enter the cochlea via the oval window, creating pressure waves in the cochlear fluid. Due to the oval window’s smaller surface area compared to the eardrum, pressure and, consequently, sound intensity are amplified.
• The cochlea contains the basilar membrane lined with hair cells. Movement of these cells generates electrical impulses that travel along the auditory nerve to the brain. Different frequencies activate different regions of the cochlea.
• The round window flexes to relieve pressure from cochlear fluid movement.
• The semi-circular canals, filled with fluid, detect motion and help maintain balance.

The overall transmission of sound from the outer ear to the brain can be summarised as:

Transmission of sound in the outer ear:

1. The pinna gathers sound waves and funnels them into the auditory canal, concentrating energy and amplifying intensity.
2. As the waves move through the canal, variations in air pressure cause the tympanic membrane to vibrate in sync with the incoming wave pattern.
3. A stationary wave forms in the canal, which behaves like a closed-end tube: a node forms at the eardrum and an antinode at the open end.
4. This resonance effect enhances sensitivity to certain frequencies, especially between which includes much of human speech.
5. This natural amplification contributes to the ear’s ability to detect sounds across a broad range, roughly to

Transmission of sound in the inner ear:

1. Vibrations from the oval window enter the cochlea, a coiled, fluid-filled structure.
2. As vibrations travel through the fluid, the round window flexes outward to maintain pressure balance.
3. The vibrations move the basilar membrane, which varies in stiffness and width along its length.
4. As shown in the diagram, high-frequency sounds resonate near the base, while low frequencies activate regions near the apex.
5. Movement of the basilar membrane bends hair cells, triggering nerve impulses.
6. The signals are sent through the auditory nerve to the brain, where different frequencies are interpreted as distinct sounds.

The decibel (dB) scale measures how the ear perceives changes in sound intensity.

The ear is most sensitive to sounds near frequencies near this require very low intensity to be heard. At much higher or lower frequencies, the sound must be significantly more intense to be detected.

This can be illustrated by plotting the threshold of hearing at various sound frequencies and intensities. The lowest point of this curve (the lowest intensity for a sound to be heard) is at approximately

The decibel scale is logarithmic, meaning every 10 dB increase corresponds to a tenfold increase in intensity.

For example:

• 0 dB () = threshold of hearing
• 30 dB () = quiet conversation
• 60 dB () = normal speech
• 90 dB () = loud music
• 120 dB () = threshold of pain

This scale reflects how the ear perceives sound: a tenfold increase in intensity corresponds to one equal step in loudness. For example, a sound at 30 dB is 10 times as intense as one at 20 dB, but it only seems slightly louder. A sound at 60 dB is 1000 times more intense than one at 30 dB, but it is perceived as only about twice as loud.

The threshold of hearing () is defined as at and is assigned 0 dB.

To convert an intensity , expressed in , to intensity level , expressed in decibels (dB), use the following expression:

Decibel values cannot be directly added when combining multiple sounds because the decibel scale is logarithmic, not linear.

To find the total sound intensity, first convert all decibel values to intensity in using:

Once all individual intensities are in they can be added together.

The total can then be converted back into decibels using:

When comparing the intensity of two sounds, the difference in sound level , in dB, can be calculated using the logarithmic formula:

Where:

• is the difference in sound level (dB),
• is the intensity of sound 1 in and
• is the intensity of sound 2 in

This formula is useful when you know the intensities of two different sounds and want to find out how many decibels louder one is compared to the other.

You can also rearrange this formula to find the ratio of two intensities when a difference in decibel level is known:

This tells you how many times more intense one sound is compared to another, for a given decibel difference.

The human ear detects a wide range of frequencies between and but how we perceive them (i.e. their loudness) depends on the frequency and on the intensity level.

Equal-loudness curves (see diagram) show the intensity levels (in dB) required for different frequencies to be perceived as equally loud. In other words, any two points on the same curve are perceived as equally loud.

These curves are plotted using logarithmic axes for both frequency and intensity.

They help us understand how loudness perception changes across the frequency spectrum.

The shape of the curves can vary from person to person and is influenced by many factors, such as age, hearing loss, and background noise.

The curve shows that:

• The ear is not sensitive to very low frequencies, so we are not aware of physiological noises such as blood flow.
• The ear is also not sensitive to very high frequencies.
• The ear is very sensitive between and , and most sensitive at

Hearing loss can result from several causes: ageing, excessive noise exposure, genetics or illness.

As shown in the graph below, each cause affects different frequency ranges.

• Age-related hearing loss affects all frequencies, but high frequencies are most affected.
• Noise-induced hearing loss targets the frequency range of exposure, with the most significant damage often near

Understanding these patterns helps diagnose hearing loss and design hearing aids or protection strategies for at-risk groups.

Equal loudness curves can help diagnose the types and extent of hearing loss.

A subject’s curve is compared to a standard curve for normal hearing:

• Curve A: A healthy young person with no hearing loss.
• Curve B: An older person with age-related loss (most loss at high frequencies).
• Curve C: A young person with noise-induced damage, showing the greatest loss near 4 kHz.

These curves show the shift in sensitivity and allow clinicians to quantify hearing loss. An inverted decibel curve may also be used to show the reduction in ear sensitivity at specific frequencies.