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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
It is inappropriate to consider low-frequency sound waves as traveling in rays because of their tendency to diffract around obstacles. Due to the larger wavelengths of low-frequency sound, straight-line ray prediction is ineffective. However, for higher-frequency sound and light, as their wavelengths are comparatively smaller, the diffraction effects are often negligible and the ray approximation can be applied, simplifying the prediction and analysis of these waves' behaviours.

Step by step solution

01

Understanding wave behaviour at different frequencies

Sound waves are mechanical waves that require a material medium for their propagation. The behaviour of sound waves depends on their frequency. At low frequencies, sound waves often spread out or 'diffract' around objects and obstacles in their path. This behaviour, known as diffraction, makes it difficult to represent these waves as straight lines or rays.
02

Understanding the concept of ray approximation

Ray approximation or geometric optics treats waves as straight lines or rays. It is a method used to explain the behavior of light and sound waves in certain conditions. In this implicit approximation, the wave nature of light or sound is often neglected for simplicity and convenience, and the path of wave propagation is treated as 'rays' following straight lines.
03

Correlating high frequency and ray approximation

For higher frequencies, like light or high-frequency sound waves, the diffraction effects are often negligible as the wavelengths of these waves, relative to the obstacles they encounter, are small. Hence, ray approximation can be used in these cases effectively to simplify the analysis and make predictions about the behaviour of these waves.

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