Welcome to practical physicsPracticle physics - practical activities designed for use in the classroom with 11 to 19 year olds
 

Path differences and phase difference

Demonstration

An experiment to show how path differences between waves affects their wave phase, which is key to understanding superposition of the waves at points where the waves cross.

Apparatus and materials

  • signal generator        
  • loudspeaker
  • microphones, 2
  • double beam oscilloscope (sensitivity of 1cm for 10 mV required)
  • metre rule
  • leads

Health & Safety and Technical notes


path difference and phase difference apparatus

Set up the apparatus as shown above.

If the oscilloscope has the appropriate facility for adding signals, it could be used to display the resultant obtained by adding the two signals for various phase differences.

Procedure


a Set the frequency of the signal generator at about 1 kHz.
b Move one microphone (not that connected to the channel triggering the time-base) towards or away from the loudspeaker. Measure with a ruler the path differences between waves reaching the two microphones.
c The sound, from the single loudspeaker, has to travel different distances to the two microphones. Because of this, the two traces will probably not be in phase.
On the oscilloscope, observe the phase difference between the sound waves reaching the two microphones.
d For what path differences will the oscillations be (i) in phase, (ii) in antiphase (i.e. having phase difference of half a cycle)? Use this to determine the wavelength of the sound waves.

e Some double beam oscilloscopes are able to display the resultant of adding the two input signals. What resultant would you expect if you add two vibrations which are (i) in phase, (ii) in antiphase? If you have such an oscilloscope, then try this.

Teaching notes


1 The experiment could be done either as a demonstration, or as one experiment in a circus of related class experiments.
2 Note that students may find this arrangement confusingly similar to experiments involving the superposition of sound waves. Here the electrical signals produced by two microphones are being added by the oscilloscope. There is no superposition of sound waves.
3 Differing amplitudes may arise, not only because one microphone is nearer the source, but also because the sensitivities of the microphones may differ.
4 Possible discussion points:
When two or more waves simultaneously pass through one place, the displacement at that place is the sum, taking account of phase differences, of the displacements of the individual waves.
This applies so long as there is no discontinuity in the properties of the system - thus an exception arises if, for example, two ordinary waves in shallow water combine to achieve enough height to break.
If the superposing waves have equal constant frequencies, and emerge from stationary sources, then a pattern of maxima and minima is formed which is stationary in space. This is so even if there are phase differences between the sources.
If two sources have different but constant frequencies f1 and f2, then beats will occur. At any given point where the waves superpose, the amplitude of the oscillations will rise and fall at a frequency |f1 - f2|. Beats will generally be noticeable only if the values of f1 and f2 are close.

This experiment has yet to undergo a health and safety check.

Related guidance


Superposition effects as a characteristic of wave motion

Related experiments


Transverse waves on a spring
Pulses and continuous waves with a slinky spring
Transverse waves along a rope
Interference with plastic wave model