show an understanding of experiments that demonstrate two-source interference using water waves in a ripple tank, sound, light and microwaves

Interference

Interference occurs when two or more coherent waves overlap in space, producing a resultant wave whose amplitude is the vector sum of the individual amplitudes. The phenomenon is a key test of the wave nature of water, sound, light and microwaves.

Key Concepts

• Coherent sources – same frequency and a constant phase relationship.
• Path difference \$\Delta r\$ determines the type of interference.
• Constructive interference: \$\Delta r = m\lambda\;(m=0,1,2,\dots)\$
• Destructive interference: \$\Delta r = \left(m+\tfrac12\right)\lambda\$
• Fringe spacing for two‑source interference:

  \$\Delta y = \frac{\lambda D}{d}\$

  where \$d\$ is the source separation and \$D\$ the distance to the observation screen.

Experiments Demonstrating Two‑Source Interference

1. Water Waves in a Ripple Tank

A ripple tank provides a visual demonstration of interference patterns formed by two point sources.

• Apparatus: Ripple tank, two identical dippers (or a single dipper with a split barrier), strobe light, white screen.
• Procedure:

  1. Adjust the dippers so that they generate waves of the same frequency and amplitude.
  2. Observe the pattern of bright (constructive) and dark (destructive) fringes on the screen.
  3. Measure the fringe spacing \$\Delta y\$ and compare with \$\Delta y = \lambda D/d\$.

• Key observations: Straight, equally spaced nodal lines radiating from the midpoint between the sources.

2. Sound Interference (Young’s Double‑Speaker Experiment)

Sound waves from two loudspeakers can produce regions of increased and decreased intensity, audible as “loud” and “soft” spots.

• Apparatus: Two identical speakers driven by the same audio source, a microphone connected to a sound level meter, a movable rail.
• Procedure:

  1. Place the speakers a distance \$d\$ apart and align them toward the rail.
  2. Move the microphone along the rail and record the sound intensity.
  3. Identify positions of maxima and minima; calculate \$\lambda\$ using \$d\sin\theta = m\lambda\$.

• Typical result: Alternating zones of high and low sound pressure corresponding to constructive and destructive interference.

3. Light Interference – Double‑Slit Experiment

The classic Young’s double‑slit experiment provides quantitative evidence of light’s wave nature.

• Apparatus: Monochromatic laser, double‑slit slide (known slit separation \$d\$), screen, measuring ruler.
• Procedure:

  1. Align the laser so that its beam is perpendicular to the slit plane.
  2. Measure the distance \$D\$ from the slits to the screen and the fringe spacing \$\Delta y\$.
  3. Calculate the wavelength using \$\lambda = \frac{\Delta y\, d}{D}\$.

• Observations: Bright and dark fringes of equal spacing; the pattern disappears if the slits are illuminated by incoherent light.

4. Microwave Interference – Double‑Slit or Michelson Interferometer

Microwaves, with wavelengths of a few centimeters, allow interference to be observed with simple laboratory equipment.

• Apparatus: Microwave transmitter, double‑slit plate (slit separation \$d\$), movable detector, meter bridge.
• Procedure:

  1. Set the transmitter to emit a continuous wave at a known frequency (e.g., 10 GHz, \$\lambda = 3\,\$cm).
  2. Place the double‑slit plate in the beam path and position the detector at distance \$D\$.
  3. Scan the detector laterally and record the intensity variation.
  4. Use the measured fringe spacing to verify \$\Delta y = \lambda D/d\$.

• Result: Clear sinusoidal intensity pattern confirming microwave interference.

Comparison of Experiments

Summary

All four experiments illustrate the same fundamental principle: when two coherent sources emit waves of the same frequency, the superposition of their fields leads to regions of constructive and destructive interference. By measuring fringe spacing and applying the relation \$\Delta y = \lambda D/d\$, students can determine the wavelength of the wave under investigation and reinforce the wave model for water, sound, light and microwaves.