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REFRACTION OF SOUND

After reading this section you will be able to do the following:

• Define sound refraction and why it occurs.
• Describe what occurs when a sound wave reaches the critical angle.

Click here to run a JavaScript application for Snells Law.

Questions

1. What happens to sound traveling in one material when it enters another material at an angle normal to surface between the two materials (90 degrees to the surface)?
2. What happens to sound traveling in one material when it enters another material at an angle other than normal to surface between the two materials?
3. What happens to the sound as the incident angle approaches being parallel to the surface?

Sound traveling between materials

Remember that sound travels faster in some materials than others. Sound waves travel outward in straight lines from their source until something interferes with their path. When sound changes mediums (enters a different material) at an angle other that 90 degrees, it is bent from its original direction. This change in angle of direction is called refraction. Because of the angle, part of the wave enters the new medium first and changes speed. The difference in speeds causes the wave to bend. The velocity of sound in each material is determined by the material properties (elastic modulus and density) for that material.

In the animation below, a series of plane waves are shown traveling in one material and entering a second material that has a higher acoustic velocity. Therefore, when the wave encounters the interface between these two materials, the portion of the wave in the second material is moving faster than the portion of the wave in the first material. It can be seen that this causes the wave to bend.

The angle of refraction depends on the angle that the waves has when it enters the new medium and the velocities of the waves in the two materials. Snell's Law describes the relationship between the angles and the velocities of the waves.  Snell's law equates the ratio of material velocities V1 and V2 to the ratio of the sine's of incident (Q1) and refracted (Q2) angles, as shown in the applet above and in the following equation.

 Where: VL1 is the longitudinal wave velocity in material 1. VL2 is the longitudinal wave velocity in material 2.

It should be noted that only a portion of the sound enters the second medium.  A portion of the sound is also reflected back into the first medium. The angle which the incident wave makes with a line normal to the interface is equal to the angle which the reflected wave makes to the same normal line.  It should also be noted that when the angle of the incident wave reaches a large enough angle, the sound wave no longer enters the second material but instead the wave runs along the interface between the two materials. The angle where this occurs is called the critical angle.