Wave Interference: Principles and Experimental Analysis

Wave Interference

Objectives

• Study the phenomenon of wave interference from two slits and two point sources.
• Analyze how interference patterns vary with wavelength and slit separation.

Planning

Wave interference was studied on the water surface using mechanical transverse waves, which propagate perpendicular to the direction of energy transfer. Waves are generated by the vibration of a flat bar or two point sources (gummies).

Different angular positions satisfy the following equations:

1. d sin θ_m = mλ (where m = 0, ±1, ±2...)

Where:

• d = Distance between the slits
• θ_m = Angular position of the m-th order maximum
• y_m = Distance from the central maximum to the m-th order maximum
• S = Distance from the slit to the screen
• λ = Wavelength
• m = Order of the maximum

For a screen:

2. y_m = mλS / d

The generator is installed with a bar at a frequency of 10 Hz and an amplitude of 4.

Procedure

Part 1: Interference in Two Openings

1. Place 3 reflectors in a line with a separation of 2 cm between each. Trace the position of the reflectors on paper and draw the wave paths through the openings. Locate the areas of reinforcement (constructive) and cancellation (destructive).
2. Replace the main reflector while maintaining a slit width of 2 cm.
3. Increase the frequency to position J.

Observations:

• What happens to the wavelength?
• How does the angle of expansion change with this new wavelength?
• With a large bar, the angle is smaller than with a small barrier. For a small barrier, the longitudinal wave d is greater than that formed by the larger barrier.

Data points: λ = 0.15, θ = 4.37; λ = 0.26, θ = 7.74.

Part 2: Interference with Two Point Sources

1. Replace the straight barriers with two point sources.
2. Repeat the steps from Part 1 and compare the charts.

Analysis:

With increasing frequency, the angle decreases, indicating an inversely proportional relationship. Regarding wavelength, higher frequency results in a lower wavelength, also showing an inverse correlation. By increasing the distance between the two sources, the angle decreases compared to the previous case, while the wavelength increases, demonstrating a directly proportional relationship.

Data points: λ = 0.61, θ = 5.89; λ = 0.52, θ = 5.03.

Conclusion

A greater slit distance d results in a smaller angular position between the maxima. Additionally, the distance from the central maximum y_m decreases as d increases. As frequency increases, the wavelength and the expansion angle decrease. Point sources behave analogously to the slit experiment, producing very similar interference patterns and angular positions.