PhysicsLAB: Ripple Tank Sample Solutions

Law of Reflection

θ_i is the angle of incidence measured from the normal.
θ_r is the angle of reflection measured from the normal.

All waves obey this relationship that θ_i = θ_r

Plane Waves Reflecting off of a Parabolic Barrier

Notice that during the reflection of plane wavefronts off of a parabolic barrier, neither the frequency nor wavelength change. However, the wave shape changes from plane to circular.

Plane waves reflected off of a parabola are reflected as circular waves towards the focus of the parabola.
Circular waves generated at the focus of the parabola are reflected as plane waves.

Notice that this construction obeys the law of reflection; that is, the angle of incidence equals the angle of reflection.

Circular Waves Reflecting off of a Straight Barrier

It appears as if each reflected wavefront is being generated at an image source, S', which is as far behind the barrier as the original point source, S, is in front of the barrier.

Notice that during the reflection of circular wavefronts off of a straight barrier, neither the frequency, wavelength, nor wave shape change.

Notice that this construction obeys the law of reflection; that is, the angle of incidence equals the angle of reflection.

Two-Point Source Interference

The central region of constructive interference is known as the central maximum, or A_o. On either side of the central maximum are the first order nodes, N₁. These are regions of destructive interference. On either side of N₁ are the next antinodes, A₁. This alternating pattern of nodes and antinodes continues throughout the construction.

One way to change the amount of interference produced by two in-phase point sources is to change their separation distance but leave their frequency unchanged.

When two in-phase point sources are moved closer together, there is less interference produced, as evidenced by fewer nodes. When the amount of interference decreases, the width of any given antinode increases.
When two in-phase point sources are moved further apart, there is a greater amount of interference produced, as evidenced by a larger number of nodes. When the amount of interference increases, the width of any given antinode decreases.

Another way to change the amount of interference produced by two in-phase point sources is to change their frequency but leave their separation distance unchanged.

When the frequency is increased, more interference is produced since the wavelengths will decrease, generating more wavefronts between the two sources (the equivalent to moving the point sources further apart).
When the frequency is decreased, less interference is produced since the wavelengths will increase, generating fewer wavefronts between the two sources (the equivalent to moving the point sources closer together).

Diffraction

Diffraction is the bending of a wave around an obstacle or through an opening. The closer the obstacle/opening is to the wave's wavelength, the greater the amount of diffraction. The amount of diffraction decreases as the curvature of the diffracted wavefront decreases and the calm area behind the obstacle/opening increases.

Notice that during the diffraction of plane wavefronts through an opening, neither the frequency nor wavelength change. However, the wave shape changes from plane waves to circular wavefronts.

For narrow openings, the center of the opening acts as a point source.
For wider openings, the edges of the opening act as two VERY DISTANT in-phase point sources. This results in the appearance that the plane wavefront has essentially passed through the opening unchanged, with just a little bit of bending, ir diffraction, on the edges.

Depending on the relative size of the opening compared to the wavelength, interference fringes can sometimes be seen within the diffraction pattern.

Refraction

Refraction is the bending of a wavefront resulting from a change in wave speed. This occurs when there is an abrupt change in the medium through which the waves are traveling.

Notice that during the refraction of plane waves across an oblique interface, neither the frequency nor wave shape change. However, the wavelength decreases in the slower medium, the shallow water. This decrease is caused by a reduction in the wave's speed.

When a wave is refracted upon entering a slower medium, we say that it is "bent towards the normal." Note in the above diagram how the angle of refraction, θ_r, is smaller than the angle of incidence, θ_i.