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 waterapprox0.1478m

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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