Waves

Frequency, Wavelength, Amplitude, and Wave Speed

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A wave is a disturbance that transfers energy through a medium (or through empty space for electromagnetic waves) without transferring matter. The particles of the medium oscillate around their equilibrium positions while the wave pattern moves forward. Understanding waves is fundamental to acoustics, optics, seismology, and quantum mechanics.

Transverse waves oscillate perpendicular to the direction of travel (like water waves or light). Longitudinal waves oscillate parallel to propagation (like sound). Both obey the same wave equation: $v = f\lambda$ . When two waves meet, they superpose - their displacements add - producing interference patterns that are central to many modern technologies.

Key Facts

Wave equation: $v = f\lambda$ (speed = frequency $\times$ wavelength)
Transverse waves: oscillation is perpendicular to wave travel direction.
Longitudinal waves: oscillation is parallel to wave travel direction (e.g. sound).
Constructive interference: waves in phase add to produce larger amplitude.
Destructive interference: waves out of phase cancel each other.
Wave speed depends on the medium, not the frequency.

Vocabulary

Wavelength (λ): Distance between two consecutive points in phase (e.g. crest to crest).
Amplitude: Maximum displacement from equilibrium; related to energy, not speed of the wave.
Frequency: Number of complete wave cycles passing a point per second, in hertz (Hz).
Interference: The superposition of two or more waves; produces regions of reinforcement or cancellation.
Standing wave: A pattern produced when two identical waves travel in opposite directions and interfere to form nodes and antinodes.

Common Mistakes to Avoid

Confusing wave speed with particle speed. Wave speed ( $v = f\lambda$ ) is how fast the pattern moves; particle speed is how fast individual medium particles oscillate.
Thinking increasing frequency increases wave speed in the same medium. Speed depends on the medium's properties, not the frequency.
Believing destructive interference destroys energy. Energy is merely redistributed - bright fringes in double-slit experiments are brighter to compensate for dark fringes.
Applying the wave equation $v = f\lambda$ when units are inconsistent - always check that $\lambda$ is in meters when $v$ is in m/s.

Practice Questions

1 Sound travels at 340 m/s. What is the wavelength of a 440 Hz (concert A) tone?
2 A wave on a string has a period of 0.02 s and a wavelength of 1.5 m. What is its speed?
3 Two speakers emit the same frequency in phase. At a point where the path difference is 1.5λ, is the interference constructive or destructive?

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