A plane sound wave in air at 20 degree C, with wavelength 589 mm, is incident on

Question

A plane sound wave in air at 20 degree C, with wavelength 589 mm, is incident on a smooth surface of water at 25 degree C at an angle of incidence of (a) Determine the angle of refraction for the sound wave. (b) Determine the wavelength of the sound in water. 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 12.90. (c) Determine the angle of refraction. (d) Determine the wavelength of the light in water. (e) Compare and contrast the behavior of the sound and light waves in this problem.

Explanation / Answer

the first answer makes a classic error...to use the indices of refraction of light in air and water; this question asks about sound waves the speed of sound in water is GREATER than the speed of sound in air by a factor of about 4.3 times so, in using snell's law of refraction: n1 sinx1 = n2 sinx2 where n1 is the index of refraction of sound in air n2 is the index of refraction of sound in water x1=angle of incidence and x2=angle of refraction we want to find: sin x2=(n1/n2) sinx1 we know that n1/n2=v2/v1 where v2, v1 are the speeds of sound in water, air we have that sinx2=(4.3)sin x1 sinx2=(4.3)sin13=15.9 deg wavelength = speed/frequency so if the speed increases by a factor of 4.3 (since the frequency stays the same,), the wavelength increases by the same factor and the new wavelength is then new wavelength = 4.3x0.589 m = 2.53m

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