A plane sound wave in air at 20^∘ C, with wavelength 589 mm, is incident on a smooth surface of

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A plane sound wave in air at 20^∘ C, with wavelength 589 mm,...

A plane sound wave in air at $20^{\circ} \mathrm{C},$ with wavelength $589 \mathrm{mm},$ is incident on a smooth surface of water at $25^{\circ} \mathrm{C}$ at an angle of incidence of $3.50^{\circ} .$ Determine the angle of refraction for the sound wave and the wavelength of the sound in water. Compare and contrast the behavior of the sound in this problem with the behavior of the light in Problem $9 .$

Key Concepts

Wavelength, Frequency, and Speed Relationship

The relationship among wavelength, frequency, and speed (v = ?f) is fundamental to all wave phenomena. When a wave passes from one medium into another, its frequency remains constant, but if the wave speed changes due to different medium properties, the wavelength must also change correspondingly.

Comparison of Sound and Light Refraction

Both sound and light waves undergo refraction at the interface between different media, following a law analogous to Snell's Law. However, while light is an electromagnetic wave whose speed is largely fixed by the medium's optical properties, sound is a mechanical wave whose speed depends on the medium's physical properties such as temperature and density. This leads to differences in how each type of wave interacts with the boundary.

Wave Refraction

When a wave travels from one medium to another, its speed generally changes, which causes the direction of the wave to change. This bending of the wave is called refraction. The degree of bending depends on the relative speeds of the wave in the two media.

Snell's Law

Snell's Law provides the quantitative relationship between the angle of incidence and the angle of refraction when a wave passes across an interface between two different media. While commonly associated with light, it applies equally to sound waves, with the ratio of the sine of the angles proportional to the ratio of the wave speeds in the two media.

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