Chapter 7: Wave Behavior

In this chapter (the longest in the book!) we investigate the behavior of waves in various circumstances. Some of our examples will be for light but remember that all waves have similar behavior; sound waves will also obey the laws of reflection and refraction, scattering, diffraction, interference, etc.

Key Terms:

Reflection, specular and diffuse reflection, refraction, constructive and destructive interference, path difference, diffraction, dispersion, Doppler shift, standing waves, scattering, beats, ultrasound.

7a: Reflection

In many cases waves of all types will travel in a straight line, reflecting off of objects and surfaces at the same angle that they strike the surface. This is called the law of reflection and is true for sound waves as well as light as long as the surface is smooth relative to the wavelength. In the pictures below the arrows show the direction the light or sound is traveling. On the left for reflection off a smooth flat surface the angle of incidence, θ_i equals the angle of reflection, θ_r.

The law is still obeyed for a smooth curved surface but with a different result as shown in the figure on the right. In this case rays starting from one special point called the focal point still obey the law of reflection but they end up traveling outward parallel to each other. If we reverse the rays they will arrive parallel but all reflect through the focal point. Flashlights have curved mirrors behind the bulb with the bulb at the focal point so that the light coming from the flashlight is approximately a parallel beam. Outdoor concert shells are often built with a curved shape with the performer located at the focal point. This is so the sound is directed outward and spread evenly in the direction of the audience.

In the two pictures below the blue lines give the direction the wave is traveling and the small gray lines represent the crests of the waves (so the distance between the gray lines is the wavelength). For specular reflection (picture on the left) the surface is smooth relative to the size of the wave and the entire wave obeys the law of reflection. For diffuse reflection (picture on the right) the surface is rough relative to the size of the wave and, while individual components of the wave obeys the law of reflection, the wave as a whole is broken up by the reflection. To avoid strong echoes and other unwanted acoustic effects, surfaces in concert halls are designed to absorb sound and also to reflect sound diffusely, as we will see later.

Video/audio examples: