# Engineering Acoustics/Hearing Protection

## Introduction

The human ear is in constantly exposed to noise. In some situations, the
intensity of this noise can be infuriating, like on a subway, a train,
or a plane. One may want to put on headphones, and crank up the music
volume to overcome the maddening turbojet engine noise or the roar of
the city. In the cabin of an aircraft, the intensity of the noise during
cruise condition is about 85 dB, while reaching over 100 dB during
take-off and landing. A solution to reduce the exposure to high noise
levels is the use of noise-canceling headphones.

## Noise Control Mechanisms

There are two types of noise-canceling headphones. One using passive
elements, the other one making use of active elements.

### Passive Noise Control

Passive noise control elements do not require any source of energy. The
noise reduction comes from the material and the shape of the hearing
device. An example of headphones only using a passive element to block
sound are the earmuffs and ear plugs worn by workers on construction
sites. This type of headphones can reduce the noise level by about 15 to
25 decibels [^1].

The hearing protection device acts as a sound barrier. Sound barriers
are more effective with high frequency noise. Large wavelength noise, or
low frequency sounds, can bend around the device more easily, while high
frequency sound will be diffracted. An important factor in how well the
headphones will block the outside noise is how good the seal created is.
For the same pair of headphones or earphones, the attenuation can be
very good or bad, depending on how they fit on the user.

The phase speed of the device is described by the bulk speed[^2],

$c^2=\frac{(\mathcal{B}+\frac{4}{3}\mathcal{S})}{\rho_0}$

where $\mathcal{B}$ and $\mathcal{S}$ are the bulk and shear moduli of
the solid. $\rho_0$ is its density. The reflection coefficient in a
solid can be described as
$\mathbf{R}=\frac{\frac{r_n-r_1}{\cos{\theta_i}}+jx_n}{\frac{r_n+r_1}{\cos{\theta_i}}+jx_n}$

where $r$ and $n$ denote the specific acoustic resistance and reactance,
respectively. The specific acoustic resistance is

$r=\rho c$

The subscripts $n$ and $1$ denote the property in the normal direction
and of the first medium, respectively. With the reflection coefficient,
the level of attenuation and level of transmission can be found. The
power transmission coefficient is

$T_\pi(\theta)=\frac{1}{1+[(\omega \rho_s / 2r_1)\cos{\theta}]^2}$

### Active Noise Control

What makes noise-canceling headphones such an interesting device is the
use of the active element to eliminate undesirable noise. It is
important to note that a typical active noise-canceling headphone will
also have a passive element that will serve as a first barrier to the
unwanted, high frequency sound waves. Behind the noise barrier, a
combination of microphone, electrical circuit, and speaker is set in
place to destroy some of the noise that made it through the passive
element. The steps to cancel the undesirable noise are fairly
straightforward. First, the microphone detects the noise coming from
outside. Then the electrical circuit reads the information coming from
the microphone and creates a noise signal that has the same frequency
and amplitude as the outside noise, but with a phase of 180° to the
outside source. This signal is sent to the loudspeaker, which will put
out the desired sound[^3]. What happens then is the outside sound waves
get canceled -- or destroyed -- by the sound waves generated by the
speaker. The difficult part is the implementation of the system. The
limiting factor in the efficiency of noise cancelling devices is the
reaction time of the system. \"Coming within 25 degrees of the needed
180-degree phase shift can cut noise by 20 decibels. Headphones that
react more slowly provide less cancellation.\"[^4] claims Mark
Fischetti. Active noise control is effective at low frequencies. For
higher frequency noise, the required response time of the system is too
small for the device to be able to destroy the incoming sound waves.
Such a system is feasible but require complex electronics, difficult to
implement in a relatively small device.

In their studies on different brands of noise-cancelling headphones, L.
Y. L Lang et al. showed that active noise are \"reliable in stationary
noise environments as opposed to those in environment that are highly
transient.\"[^5] In situations with highly transient sound, like in an
airport or inside the cabin while the aircraft is taking off, the active
noise-control system can sometimes become ineffective, or even increase
the sound pressure level. They found that a certain pair of headphones
increased the sound pressure level by 20.4 dB at a frequency of around
600 Hz. In transient noise environment, the headphones can show
fluctuations in the level of attenuation of sound pressure, especially
in the range of 100 Hz to 1000 Hz. The efficiency of the
noise-cancelling headphones can be calculated by finding the insertion
loss. The insertion loss is measured by finding the difference in sound
pressure level in the ear when no headphones are worn and when the
active noise-cancelling device is activated and worn over the ears.

$IL_{T}=L_{0}-L_{C-ON}$

In this equation, $IL_{T}$ is the total insertion loss, $L_{0}$ is the
sound pressure level without the headphones and $L_{C-ON}$represents the
sound pressure level when the ears are covered and the active element is
turned on. The active noise-cancelling headphones have the highest
insertion loss at frequencies below 230 Hz. This is a perfect solution
for usage of headphones while commuting. In an aircraft cabin or a bus
cabin, the sound pressure level is maximum at around 110 Hz. By having
the maximum attenuation at those frequencies, one can protect their ears
from the possibly dangerous noise level found in different
transportation methods.

On top of canceling low frequency noise, noise-cancelling headphones can
improve speech intelligibility. By attenuating low frequency sound
waves, the frequencies located between 500 Hz and 1500 Hz can be
isolated leading to a more intelligible speech. In their 2001 report,
Mongeau, Bernhard and Feist concluded that noise-cancelling headphones
could be a solution to improve communication at noisy toll booth, where
car and truck noise can lead to difficult conversations[^6]. The report
states that a good communication system could raise the speech
intelligibility index (SII) up to 0.75. In regular conditions in a toll
booth, the SII can be as low as 0 when using a regular or raised vocal
effort, or 0.06 when using a loud voice. In perfect conditions, the SII
is equal to 1. Although noise-cancelling devices improve speech
intelligibility, the main issue was the reception of the idea. Having
someone wearing a pair of over-the-ear headphones while serving a client
does not give a good impression as people tend to think the attendant is
also focusing on something else.

Since it is an active system, energy must be added to the system, so the
headphones require an energy source such as a typical battery.

## Types of headphones

There are three different design of headphones. First, the one providing
the least amount of noise attenuation is the supra-aural headphone. This
type of headphone simply sits on the ears. While it is not efficient in
blocking the noise, it provides a more natural sound. The fact that it
is more open to the outside environment allows the headphones to sound
more like a speaker.

The next type is the circumaural headphone. This type of headphones fits
around the user's ears, completely isolating them. They provide good
sound attenuation because they can block sound coming from all
directions. On the other hand, they are usually heavier and not as
comfortable. Due to the size of the circumaural headphones, it is
possible to add an active element to even further decrease outside
noise. This will be discussed in the next section.

Finally, the last type is the in-ear headphone. They are worn directly
in the ear. There are two styles of in-ear headphones. The ear buds are
worn in the opening of the ear, while the canal earphones are worn in
the ear canal. This type provides the best passive noise attenuation as
they can efficiently create a seal and block the outside noise. They
also provide a high-quality sound.

## Conclusion

The noise-canceling headphones are a good example of how theoretical
science can be applied and used to solve an everyday problem. With the
speaker-generated sound wave having the same amplitude and frequency as
the outside sound waves, but with a phase difference of , the two sound
waves cancel each other and the result is a quieter commute, safer for
the ears and the mind.

## Reference

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[^1]: M. Fischetti, \"Noise-canceling headphones. Reducing a roar,\"
    *Scientific American,* vol. 292, no. 2, pp. 92-3, 2005.

[^2]: L. E. Kinsler, A. R. Frey, A. B. Coppens and J. V. Sanders,
    Fundamentals of Acoustics, United States of America: John Wiley &
    Sons, Inc., 2000.

[^3]: W. Harris, \"How Noise-canceling Headphones Work,\" 15 February
    2007. \[Online\]. Available:
    https://electronics.howstuffworks.com/gadgets/audio-music/noise-canceling-headphone.htm.
    \[Accessed 25 February 2018\].

[^4]:

[^5]: L. Y. L. Ang, Y. K. Koh and H. P. Lee, \"The performance of active
    noise-canceling headphones in different noise,\" *Applied
    Acoustics,* no. 122, pp. 16-22, 2017.

[^6]: L. Mongeau, R. J. Bernhard and J. P. Feist, \"Noise Control and
    Speech Intelligibility Improvement of a Toll Plaza,\" The Institute
    for Safe, Quiet and Durable Highways, West Lafayette, Indiana, 2001.
