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.

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 ,

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

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. 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." 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." 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. 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.