Wave Properties and Wave Speed

Why Wave Models Matter

The Physical Science: Physics Regents treats waves as models for carrying energy and information. A cluster may show water ripples, sound data, a light ray, or an electromagnetic signal. Before calculating, decide what kind of wave is being described, which medium is involved, and what the graph or diagram actually measures.

The 2025 Physics Reference Tables give the core relationships, but the exam expects you to choose the relationship from the situation. A table of crests passing a point points toward frequency or period. A drawing with distances between crests points toward wavelength. A boundary between materials points toward speed and refraction.

Basic Wave Vocabulary

A wave is a repeating disturbance that transfers energy without transporting matter across the full distance. In a rope pulse, pieces of rope move locally while the pulse travels along the rope. In a water wave, surface water moves in small paths while the wave pattern moves outward.

Use this table to sort the common quantities:

Frequency and period are reciprocals: f = 1/T and T = 1/f. If four pulses pass a sensor each second, the frequency is 4 Hz and the period is 0.25 s. Do not add period and frequency; they describe the same timing from opposite viewpoints.

Wave Speed From the Reference Tables

The wave-speed relationship is v = f lambda. Frequency in hertz means cycles per second, and wavelength in meters means meters per cycle. Multiplying gives meters per second because the cycle count cancels.

For example, a wave with frequency 8.0 Hz and wavelength 0.50 m travels at 4.0 m/s. If the period is given instead, first find frequency. A period of 0.20 s means f = 1/0.20 s = 5.0 Hz; then use the speed relationship.

Regents distractors often reverse the operation. If the prompt asks for wavelength, rearrange to lambda = v/f. If it asks for frequency, rearrange to f = v/lambda. Check units before trusting the number.

Medium Controls Speed

A mechanical wave needs a material medium. Sound needs air, water, metal, or another material. Water waves need water. The speed of a mechanical wave depends on properties of the medium, such as stiffness, density, and temperature.

Electromagnetic waves do not require a material medium. In a vacuum, all electromagnetic waves travel at c = 3.00 x 10^8 m/s, the reference-table speed of light. Light travels more slowly in materials, which is why refraction and index of refraction matter in optics.

When a wave crosses from one medium to another, the source still determines the frequency. The speed changes because the medium changes. Since v = f lambda, a lower speed with the same frequency means a shorter wavelength.

Source, Boundary, and Medium Questions

A Regents cluster may hide the key clue in the setup. If the same vibrating source sends waves into deep water and shallow water, the frequency stays tied to the source while speed changes with water depth. If two students compare waves in different springs, the spring properties affect speed, so wavelength comparisons are fair only when the frequency is known.

Transverse and Longitudinal Motion

A transverse wave has disturbance perpendicular to the direction the wave travels. A rope wave moving horizontally while the rope moves up and down is transverse. Electromagnetic waves are also modeled as transverse waves, with oscillating electric and magnetic fields.

A longitudinal wave has disturbance parallel to the direction the wave travels. Sound in air is the most important Regents example. Air pressure compressions and rarefactions move outward while air molecules vibrate back and forth along the same line.

A diagram may show particle motion and wave direction. Keep those separate. The direction particles wiggle is not always the direction energy travels.

Graphs and Wave Evidence

A displacement-position graph freezes the wave at one instant. The horizontal distance from crest to crest is wavelength. The vertical distance from equilibrium to crest is amplitude.

A displacement-time graph watches one point in the medium. The time from crest to crest is period. Count cycles per second to find frequency.

A strong constructed response names the graph feature. Write that the crest spacing is 0.40 m, so the wavelength is 0.40 m, rather than only writing a number.

Amplitude, Energy, and Common Traps

Amplitude often connects to energy qualitatively. A louder sound has greater pressure amplitude than a quieter sound. A brighter light source emits more electromagnetic energy per second than a dimmer source. Still, amplitude is not part of v = f lambda.

If two waves have the same frequency and travel in the same medium, the larger-amplitude wave is not faster. If a source vibrates faster in the same medium, frequency increases and wavelength decreases when speed stays the same.

Before answering a Regents wave item, ask three questions: Is the graph showing position or time? Is the wave staying in one medium or crossing a boundary? Is the question asking for timing, spacing, speed, or energy? Those questions usually identify the model.