The wave equation v = fλ connects three measurable properties of a traveling wave: its speed, frequency, and wavelength. It matters because the same relationship describes sound waves, water waves, light waves, and waves on strings. When you can read a wave diagram, you can connect a picture of a wave to real physical quantities.
This makes the equation useful for solving problems and for understanding how energy and information move.
Key Facts
- Wave speed equation: v = fλ
- v = wave speed, measured in meters per second, m/s
- f = frequency, measured in hertz, Hz, where 1 Hz = 1 cycle/s
- λ = wavelength, measured in meters, m, from crest to crest or trough to trough
- Period and frequency are reciprocals: f = 1/T and T = 1/f
- Amplitude is the maximum displacement from the equilibrium line, not the distance from crest to trough
Vocabulary
- Wave speed
- Wave speed is the distance a wave pattern travels per unit time.
- Frequency
- Frequency is the number of complete wave cycles that pass a point each second.
- Wavelength
- Wavelength is the distance between matching points on neighboring cycles, such as crest to crest.
- Period
- Period is the time needed for one complete wave cycle to pass a point.
- Amplitude
- Amplitude is the maximum distance a point on the wave moves from its equilibrium position.
Common Mistakes to Avoid
- Using the distance from crest to trough as wavelength. That distance is half a wavelength for a sinusoidal wave, while wavelength is measured from crest to crest, trough to trough, or any matching point to the next matching point.
- Confusing amplitude with wavelength. Amplitude is a vertical displacement from equilibrium, while wavelength is a horizontal distance along the direction the wave travels.
- Forgetting that frequency and period are reciprocals. If the period gets larger, the frequency gets smaller, so use f = 1/T or T = 1/f rather than adding or multiplying them directly.
- Mixing units in v = fλ. Frequency must be in hertz and wavelength must be in meters if wave speed is expected in meters per second.
Practice Questions
- 1 A wave has a frequency of 8.0 Hz and a wavelength of 2.5 m. What is its wave speed?
- 2 A water wave travels at 12 m/s and has a wavelength of 3.0 m. Find its frequency and period.
- 3 Two waves travel through the same medium at the same speed. Wave A has a longer wavelength than Wave B. Which wave has the lower frequency, and why?