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Chapter 30: Problem 1

Why is it usually inappropriate to consider low-frequency sound waves as traveling in rays? Why is the ray approximation more appropriate for high- frequency sound and for light?

Short Answer

Expert verified
Ray approximation, wherein light and sound are thought of as traveling in rays, doesn't usually apply to low-frequency sound waves because their long wavelengths enable them to diffract around everyday-sized objects, and so they don't act like straight-line rays. Conversely, high-frequency sound and light waves have shorter wavelengths, and provided the objects or apertures in their paths are larger than their wavelengths, they behave more like rays, thus making ray approximation appropriate.

Step by step solution

01

Understanding Ray Approximation

Ray approximation, also known as ray theory, treats light or sound as a group of rays that travel in straight lines and undergo reflection or refraction when they meet surfaces. It is a simplifying model used to analyse and calculate complex wave behaviors. However, this theory assumes that the waves are traveling in a medium where there are no dimensions smaller than the wavelength of the wave. This means that ray approximation works only when the wavelength of the wave is smaller than the obstacles or apertures in its path.
02

Why Ray Approximation Doesn't Work for Low-Frequency Sound Waves

Low-frequency sound waves have a long wavelength. In everyday situations, these wavelengths are typically larger than the objects they encounter, so they can diffract around those objects and continue to travel in many directions. Therefore, it's generally inappropriate to consider low-frequency sound waves as traveling in straight-line rays, which is a key component of ray approximation.
03

Why Ray Approximation Works for High-Frequency Sound and Light

High-frequency sound waves and light waves have short wavelengths. When the dimensions of obstacles or apertures are much larger than the wavelength, these waves behave more like rays traveling in straight lines. For these types of waves, the ray approximation applies, as the waves encounter less diffraction compared to low-frequency sound waves.

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Most popular questions from this chapter

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