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Chapter 19: Problem 30

Describe three general types of noise that have a different dependence on frequency. Give an example of the source of each kind of noise.

Short Answer

Expert verified
The three general types of noise are white noise (e.g., thermal noise), pink noise (e.g., sound of rain), and Brownian noise (e.g., Brownian motion in fluids).

Step by step solution

01

Understanding Noise in Signals

Noise in signals can affect the clarity and accuracy of information transmission. It is important to know the characteristics of different types of noise to address these issues appropriately. Noise is often categorized based on its frequency dependence.
02

Identify White Noise

White noise describes a type of noise that has a constant power spectral density across all frequencies. This means it has equal intensity at different frequencies of the frequency spectrum. An example of a source of white noise is the thermal noise generated by electronic devices, which arises from the random motion of electrons.
03

Identify Pink Noise

Pink noise, also known as 1/f noise or flicker noise, has an inverse relationship with frequency. This type of noise is characterized by equal energy per octave, meaning the power decreases with increasing frequency. Pink noise is common in electronic devices and also in natural phenomena like the sound of rain or waterfalls.
04

Identify Brownian Noise

Brownian noise, or Brown noise (also known as red noise), has its power density decreasing at 6 dB per octave with increasing frequency (which is proportional to 1/f虏). This makes it more intense at lower frequencies. An example of a source of Brownian noise is the movement of a large number of particles in a liquid or gas, which is why it is related to Brownian motion.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

White Noise
White noise is a type of noise that exhibits a uniform power distribution across all frequencies. It is like the visual equivalent of white light, which contains all colors equally.

In practical terms, this means white noise has the same intensity at every frequency, making it a flat spectral profile.
  • One of the most common examples of white noise is thermal noise, which is produced by the random movement of electrons in electrical circuits.
  • This type of noise is also likened to the static "hiss" sound you might hear on old television sets when no signal is being received.
Understanding white noise helps in various fields, including acoustics and engineering, with its predictable, constant power useful for testing audio equipment and at times even masking other disruptive noises in environments.
Pink Noise
Pink noise, often referred to as 1/f noise, is characterized by its frequency spectrum being inversely proportional to its frequency. This means it has more power at lower frequencies than at higher ones. As a result, pink noise appears smoother to human hearing, compared to white noise.
  • In nature, pink noise can be heard in the rustling of leaves, falling rain, or the steady backdrop of a waterfall.
  • Electronics can also produce pink noise, which is sometimes desirable in sound design and music production due to its more balanced and warm quality.
Scientists and engineers often study pink noise for its implications in understanding complex systems, as it is prevalent in a range of biological and physical phenomena.
Brownian Noise
Brownian noise, also known as red or Brown noise, descends in power by approximately 6 dB per octave as frequency increases. This drop-off results in significantly higher power at the lower frequency end of the spectrum.
  • Brownian noise is named after Brownian motion, exemplified by the random movement observed when particles are suspended in a fluid or gas.
  • A practical and simple example of Brownian noise can be experienced by listening to the low, rumbling sounds of a thunderstorm or distant ocean waves.
The tendency of Brownian noise to dominate at low frequencies gives it a "deeper" sound, contributing to its use in diverse fields such as music production and environmental sound recording.

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Most popular questions from this chapter

Which variables increase the resolution of a grating? Which variables increase the dispersion of the grating? How is the blaze angle chosen to optimize a grating for a particular wavelength?

fused silica is given by $$ \begin{aligned} n^{2}-1=& \frac{(0.6961663) \lambda^{2}}{\lambda^{2}-(0.0684043)^{2}}+\frac{(0.4079426) \lambda^{2}}{\lambda^{2}-(0.1162414)^{2}} \\ &+\frac{(0.8974794) \lambda^{2}}{\lambda^{2}-(9.896161)^{2}} \end{aligned} $$ where \(\lambda\) is expressed in \(\mu \mathrm{m}\). (a) Make a graph of \(n\) versus \(\lambda\) with points at the following wavelengths: \(0.2,0.4,0.6,0.8,1,2,3,4,5\), and \(6 \mu \mathrm{m}\). (b) The ability of a prism to spread apart (disperse) neighboring wavelengths increases as the slope \(d n / d \lambda\) increases. Is the dispersion of fused silica greater for blue light or red light?

. In the cavity ring-down measurement at the opening of this chapter, absorbance is given by $$ A=\frac{L}{c \ln 10}\left(\frac{1}{\tau}-\frac{1}{\tau_{0}}\right) $$ where \(L\) is the length of the cavity between mirrors, \(c\) is the speed of light, \(\tau\) is the ring-down lifetime with sample in the cavity, and \(\tau_{0}\) is the ring-down lifetime with no sample in the cavity. Ring-down lifetime is obtained by fitting the observed ring-down signal intensity \(I\) to an exponential decay of the form \(I=I_{0} \mathrm{e}^{-t / \tau}\), where \(I_{0}\) is the initial intensity and \(t\) is time. A measurement of \(\mathrm{CO}_{2}\) is made at a wavelength absorbed by the molecule. The ring- down lifetime for a \(21.0-\mathrm{cm}\)-long empty cavity is \(18.52 \mu \mathrm{s}\) and \(16.06 \mu \mathrm{s}\) for a cavity containing \(\mathrm{CO}_{2}\). Find the absorbance of \(\mathrm{CO}_{2}\) at this wavelength.

A measurement with a signal-to-noise ratio of \(100 / 1\) can be thought of as a signal, \(S\), with \(1 \%\) uncertainty, e. That is, the measurement is \(S \pm e=100 \pm 1\).

Explain how an optical fiber works. Why does the fiber still work when it is bent?
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