The Physics of Hearing

External Ear

The function of the external or outer ear is mainly to direct and amplify sound waves into the middle ear. There are three main parts of the outer ear, each of which assists in the collection or amplification of sound.

The auricle, or pinna, is the portion of the ear that protrudes from the temporal lobe of the skull and is visible as a collection of folds of skin and cartilage. The position of the auricles at angles of 30°, one on each side of the head, help the listener to localize sound and determine which direction the signal is coming from. In addition, the cup-like shape of the auricle funnels sound into the ear. Many people cup their hands over their ears to hear better because this action enhances the natural shape of the outer ear and actually amplifies the incoming sound by 5 to 8 decibels (dB).

Once through the auricle, the sound waves enter the head through the external auditory meatus, more commonly known as the ear canal. This is essentially a tube or pipe open on one side to the environment and closed on the other end by the tympanic membrane, or eardrum, which is the third component of the external ear. Because of the canal’s structure, standing waves are formed inside. A look at the physics of the external auditory meatus reveals the resonant frequency and wavelength of the canal.

The average length of the external auditory meatus (L) is 2.3 cm or 0.023 m and the speed of sound in air (v) is approximately 343 m/s. This information can be used an equation to find the fundamental frequency (f1) of a tube closed on one end:

f1 = v / (4 L)

f1 = (343 m/s) / (4 * 0.023 m)

f1 = 3728 Hz

The equation gives a resonant frequency of 3728 Hz, or cycles per second. However, because the tympanic membrane at one end of the canal both absorbs and reflects some of the energy, there is a damping effect. As a result, the resonant frequency range is actually broader, spanning a range from 3500 to 4000 Hz.

A second equation can be applied to find the wavelength (λ) of sound waves in the canal using the fundamental frequency just determined:

λ = v / f1

λ = (343 m/s) / 3728 Hz

λ = (0.092 m or 9.2 cm)

Because of these standing waves, “curves of equal loudness” are established in the external auditory meatus. This means that sounds resonating between 3500 and 4000 Hz, or subsequent integral multiples of these frequencies, require less intensity to be heard at the same loudness as other sounds of different frequencies.

 

image source: http://www.ent.uci.edu/images/How%20Ear%20Works.jpg