Superposition: (e) two-source interference with sound and microwaves

The idea

Two-source interference can be demonstrated with sound and microwaves. For sound, two loudspeakers driven by the same signal act as coherent sources; a microphone moved along a line parallel to the speakers detects alternating loud and quiet regions. For microwaves, a single transmitter feeds two horn aerials to produce coherent waves; a receiver moved along a line detects maxima and minima. In both cases, maxima occur where path difference is a whole number of wavelengths (0, λ, 2λ, ...) and minima where path difference is an odd number of half-wavelengths (λ/2, 3λ/2, ...). The fringe spacing or separation of maxima depends on wavelength, source separation and distance to the detector. Using microwaves of wavelength about 3 cm gives measurable spacings on a laboratory bench.

What earns the marks

• Two-source interference requires coherent sources: same frequency and constant phase difference.
• For sound, two loudspeakers connected to the same signal generator provide coherent sources; a microphone detects maxima and minima.
• For microwaves, a single transmitter split to two horn aerials provides coherent sources; a receiver detects maxima and minima.
• Maxima occur where path difference is a whole number of wavelengths; minima occur where path difference is an odd number of half-wavelengths.
• The spacing between adjacent maxima increases with wavelength and distance to the detector, and decreases with increasing source separation.

Common mistakes and how to put them right

• Using two independent loudspeakers or transmitters without a common signal.

  Put it right: The sources must be coherent, so they must be driven by the same oscillator or derived from the same transmitter.

• Thinking that minima are points where no sound or microwave energy arrives.

  Put it right: At minima the waves cancel at that point, but energy is redistributed to the maxima.

• Assuming the interference pattern is the same for all wavelengths.

  Put it right: Changing the wavelength changes the spacing of maxima and minima.

• Confusing the condition for maxima and minima.

  Put it right: Maxima correspond to path difference nλ, while minima correspond to (n + ½)λ.

Exam tips

• When describing an experiment, state how coherence is achieved, for example by connecting both loudspeakers to one signal generator.
• Use the wave equation v = fλ to find the wavelength from the frequency and speed of sound or microwaves before calculating path differences.
• For a given point, calculate the path difference from the source distances and compare it with λ to decide whether it is a maximum or minimum.
• Remember that the speed of sound in air is about 340 m/s and the speed of microwaves is the speed of light, 3.0 × 10⁸ m/s.