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Chapter 15: Problem 11

Noise results from the superposition of a very large number of sound waves of various frequencies (usually in a continuous spectrum), amplitudes, and phases. Can interference arise with noise produced by two sources?

Short Answer

Expert verified
Answer: Although it is theoretically possible for interference to momentarily occur in the superposition of noise waves from two sources, it is not a persistent phenomenon due to the random and continuously changing nature of the waves. Therefore, we can say that interference does not generally arise with noise produced by two sources.

Step by step solution

01

Understanding Interference

Interference is a phenomenon in which two or more waves superpose to form a resultant wave of greater, lower, or the same amplitude, depending on the phase difference between the original waves. Interference can be either constructive or destructive. Constructive interference occurs when the waves are in phase, and their amplitudes add up to form a larger amplitude wave, while destructive interference takes place when waves are out of phase and their amplitudes cancel each other out.
02

Superposition of waves from two sources of noise

Since noise is composed of a large number of sound waves with varying frequencies, amplitudes, and phases, the superposition of waves from two sources of noise would lead to an even more complex wave pattern. The resultant noise would also consist of a large number of waves with continuously changing frequencies, amplitudes, and phases.
03

Possibility of interference in noise

For interference to occur, it would require that two waves from the two different noise sources to have the same frequency and a constant phase difference. However, the nature of noise is such that the frequencies and phases are continuously changing, making it highly unlikely for two waves with the same frequency and phase difference to overlap and produce interference for any significant period of time.
04

Conclusion

Although it is theoretically possible for interference to momentarily occur in the superposition of noise waves from two sources, it is not a persistent phenomenon due to the random and continuously changing nature of the waves. Therefore, we can say that interference does not generally arise with noise produced by two sources.

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Most popular questions from this chapter

A particular steel guitar string has mass per unit length of \(1.93 \mathrm{~g} / \mathrm{m}\). a) If the tension on this string is \(62.2 \mathrm{~N},\) what is the wave speed on the string? b) For the wave speed to be increased by \(1.0 \%\), how much should the tension be changed?

The largest tension that can be sustained by a stretched string of linear mass density \(\mu\), even in principle, is given by \(\tau=\mu c^{2},\) where \(c\) is the speed of light in vacuum. (This is an enormous value. The breaking tensions of all ordinary materials are about 12 orders of magnitude less than this.) a) What is the speed of a traveling wave on a string under such tension? b) If a \(1.000-\mathrm{m}\) -long guitar string, stretched between anchored ends, were made of this hypothetical material, what frequency would its first harmonic have? c) If that guitar string were plucked at its midpoint and given a displacement of \(2.00 \mathrm{~mm}\) there to produce the fundamental frequency, what would be the maximum speed attained by the midpoint of the string?

Consider a monochromatic wave on a string, with amplitude \(A\) and wavelength \(\lambda\), traveling in one direction. Find the relationship between the maximum speed of any portion of string, \(v_{\max },\) and the wave speed, \(v\)

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A wave on a string has a wave function given by $$ y(x, t)=(0.0200 \mathrm{~m}) \sin \left[\left(6.35 \mathrm{~m}^{-1}\right) x+\left(2.63 \mathrm{~s}^{-1}\right) t\right] $$ a) What is the amplitude of the wave? b) What is the period of the wave? c) What is the wavelength of the wave? d) What is the speed of the wave? e) In which direction does the wave travel?
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