A plane sound wave in air at 20°C, with wavelength 0.645 m, is incident on a smooth surface of water at 25°C, at an angle of incidence of 3.65°. How do you determine the angle of refraction for the sound wave and the wavelength of the sound in water?

1 Answer
A08
Jan 19, 2016

Angle of refraction #theta_rapprox 0.8^o#
Wavelength in water#approx0.1478m#

Explanation:

In air at #20^o C# the speed of sound #v_s^(air) = 343m//s#.
In fresh water at #25^oC# the speed of sound # v_s^(water)=1497 m//s#

Using the following relation between angle of incidence #theta _i#, angle of refraction #theta_r#, wavelengths and velocity of the sound wave in different media

#(sin theta _i/sin theta_r)=lambda_(air)/lambda_(water)=v_(water)/v_(air)#

  1. For calculating angle of refraction the above equation between angle and velocity becomes

#(sin theta _i/sin theta_r)=v_(water)/v_(air)#

#(sin 3.65/sin theta_r)=1497/343#
# theta_r=sin^(-1)(0.06366times 343/1497)#
# theta_r=sin^(-1)(0.01459)#
2. To calculate the wavelength in water

#lambda_(air)/lambda_(water)=v_(water)/v_(air)#
Inserting the values

#0.645/lambda_(water)=1497/343#
#lambda_(water)=0.645 times343/1497#

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