Physics · Waves · Sound / Principles and Exploration
Wave interference — principles and investigation
The displacement where two waves overlap is the sum of the displacements of the two waves. Adjust amplitude, frequency, and phase difference and compare constructive and destructive interference. It is easy to understand why the size of the composite wave varies by reading not only the waveform at the same moment but also the time change at the observation point.
How does it work?
At the same frequency and amplitude, a phase difference of 0° is reinforcement, and 180°(π) is complete cancellation.
y = y₁ + y₂
Try this investigation
- Blue and orange are individual waves, and green is a composite wave. Check y₁+y₂ at the observation point.
- Observe and record the phase differences of 0°, 90°, and 180° for 4 s each at the same amplitude and frequency.
- Change and record only the amplitude or frequency of one wave.
Interpreting your results
When does a 180° phase difference fail to produce complete cancellation?
Even if the frequency is the same, if the amplitude is different, the difference in amplitude remains.
Assumptions and limitations
Add linear waves of small amplitude. The two waves are independent signals with the same spatial wavelength of 4 m. At different frequencies, the phase difference varies with time. (maximum value−minimum value)/2 during 4 s is the value of the finite observation interval. Sound is 220 times f₁.