Waves and interference
Relate frequency and wavelength, then explain reinforcement and cancellation.
Before you begin
- Wave amplitude
- Ratios and periodic motion
Connect speed, frequency and wavelength
Frequency counts cycles per second and wavelength is the distance between points in the same phase on adjacent cycles. Wave speed is their product. When a wave crosses into a different medium, its frequency is set by the source and normally remains unchanged, while speed and wavelength may change. Amplitude describes the size of the oscillation, not its repetition rate.
Apply superposition
When waves overlap in a linear medium, their displacements add. Equal in-phase displacements reinforce; equal opposite displacements cancel locally. A stable interference pattern requires a consistent phase relationship. Destructive interference at one location does not mean energy vanishes from the entire system; interference redistributes the pattern of energy transfer.
Worked example
A wave has frequency 50 Hz and wavelength 4 m. Find its speed.
Show the worked solution
- Use v = fλ with hertz as cycles per second.
- Multiply 50 × 4.
- The unit is metres per second.
200 m/s.
Try it yourself
Two equal coherent waves meet in antiphase at a point. What happens there?
Common mistakes
- Do not confuse phase difference with a change in frequency.
What can you explain now?
A wave of frequency 100 Hz enters a medium where its speed is 250 m/s. Find its wavelength.
Compare with the explanation
2.5 m.
The frequency remains 100 Hz, so λ = v/f = 250/100. The changed speed changes wavelength.
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