Aplane sound wave in air at 20°c, with wavelength 589 mm, is incident on a smooth surface of water at 25°c at an angle of incidence of 11.7°.

(a) determine the angle of refraction for the sound wave.

(b) determine the wavelength of the sound in water.

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a narrow beam of sodium yellow light, with wavelength 589 nm in vacuum, is incident from air onto a smooth water surface at an angle of incidence of 11.7°.

(c) determine the angle of refraction.

(d) determine the wavelength of the light in water.

(a). The angle of refraction for the sound wave is 61.8°.

(b). The wavelength of the sound in water is 2.56 m.

(c). The angle of refraction is 8.26°.

(d). The wavelength of the light in water is 441.75 nm.

Explanation:

Given that,

Wavelength = 589 mm

Incidence angle = 11.7°

We know that,

The speed of sound in water is GREATER than the speed of sound in air by a factor of about 4.3 times.

The speed of sound wave in water

The speed of sound wave in air at 20°C

(a). We need to calculate the  angle of refraction for the sound wave

Using Snell's law

Put the value into the formula

The angle of refraction for the sound wave is 61.8°.

(b).  We need to calculate the wavelength of the sound in water

Using formula of wavelength

Put the value into the formula

The wavelength of the sound in water is 2.56 m.

(c). We need to calculate the angle of refraction

Using formula of Snell's law

The angle of refraction is 8.26°.

(d). We need to calculate the wavelength of the light in water

Using formula of wavelength

Put the value into the formula

The wavelength of the light in water is 441.75 nm.

Hence, This is the required solution.