State the 'Wave Equation' and define its variables.

The wave equation is $v = f\lambda$, where $v$ is wave speed ($ms^{-1}$), $f$ is frequency (Hz), and $\lambda$ is wavelength (m).

How are frequency and period mathematically related?

They are reciprocals of each other: $f = 1/T$ and $T = 1/f$. As the time for one cycle increases, the number of cycles per second decreases.

What is the fundamental difference between wavelength and period?

Wavelength is a spatial measurement representing the physical distance of one wave cycle (measured in meters), whereas period is a temporal measurement representing the time duration of one cycle (measured in seconds).

How does the calculation of wave speed differ when given frequency versus when given period?

If given frequency, use $v = f\lambda$. If given period, you must first convert it to frequency using $f = 1/T$ or use the combined form $v = \lambda / T$.

When comparing a Displacement-Distance graph and a Displacement-Time graph, which one allows you to find the wave's frequency?

The Displacement-Time graph allows you to find the period ($T$), which can then be used to calculate frequency ($f = 1/T$). The Displacement-Distance graph only provides wavelength.

Why is it incorrect to measure amplitude from the trough to the crest of a wave?

Amplitude is defined as the maximum displacement from the equilibrium (rest) position. Measuring from trough to crest gives 'peak-to-peak' displacement, which is exactly twice the amplitude.

What error occurs if you assume wave speed increases when you increase the frequency of the source?

Wave speed is determined by the medium, not the source. Increasing frequency will cause the wavelength to decrease proportionally ($v = f\lambda$), keeping the speed constant.

What is a common mistake when reading the horizontal axis of a wave graph?

Failing to check the units (e.g., ms instead of s, or cm instead of m) leads to power-of-ten errors in frequency and wave speed calculations.

Define 'Frequency' in the context of wave motion.

Frequency is the number of complete oscillations or wave cycles that pass a fixed point per second, measured in Hertz (Hz).

What is the definition of 'Amplitude'?

Amplitude is the maximum magnitude of displacement of a particle in the medium from its rest position.

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5. Waves & Particle Nature of Light

Properties of Waves

Summary

Waves are oscillations that transfer energy from one location to another without the permanent transfer of matter. Understanding waves requires a precise vocabulary to describe their spatial and temporal characteristics, as well as the mathematical relationships that govern their propagation through different media.

1. Fundamental Wave Parameters

Amplitude ( $A$ ): This is the maximum displacement of a point on the wave from its undisturbed (equilibrium) position. It represents the 'strength' or intensity of the wave; for sound, it relates to loudness, and for light, it relates to brightness.
Wavelength ( $\lambda$ ): The distance between two consecutive identical points on a wave, such as from one crest to the next or one compression to the next. It is measured in meters (m) and represents the spatial periodicity of the wave.
Period ( $T$ ): The time taken for one complete cycle of the wave to pass a fixed point. It is the temporal equivalent of wavelength and is measured in seconds (s).
Frequency ( $f$ ): The number of complete wave cycles that pass a point per unit time, typically measured in Hertz (Hz), where $1\text{ Hz} = 1\text{ cycle per second}$ .

A diagram of a transverse wave showing displacement against distance. The amplitude is labeled as the vertical distance from the equilibrium line to a peak, and the wavelength is labeled as the horizontal distance between two consecutive peaks.

2. Underlying Principles & Equations

3. Methods of Analysis: Graphical Interpretation

4. Key Distinctions: Spatial vs. Temporal Properties

5. Exam Strategy & Tips

6. Common Pitfalls & Misconceptions