How does the relationship between frequency and wavelength change if the wave speed remains constant?

They are inversely proportional. If the frequency of the wave increases, the wavelength must decrease proportionally to keep the product ($v = f \lambda$) equal to the constant speed.

What is the difference between the 'Time Period' and 'Frequency' of a wave?

Frequency is the number of wave cycles passing a point per second (measured in Hertz), while the Time Period is the duration in seconds that it takes for one complete cycle to pass. They are reciprocals: $f = 1/T$.

When comparing a high-frequency radio wave to a low-frequency radio wave in a vacuum, which one travels faster?

Neither; they travel at the same speed. All electromagnetic waves travel at the constant speed of light ($3 \times 10^8 m/s$) in a vacuum, regardless of their frequency or wavelength.

What common error occurs when a frequency is given in kilohertz (kHz) in a wave speed calculation?

Students often forget to convert kHz to Hz by multiplying by 1,000. Using kHz directly in the formula $v = f \lambda$ will result in a wave speed that is 1,000 times too small.

Why is it incorrect to use the amplitude of a wave in the wave speed equation?

Amplitude measures the maximum displacement (intensity/volume) of the wave, not its spatial frequency or timing. The wave speed depends only on the medium's properties and the relationship between frequency and wavelength.

What happens to the calculated wave speed if you accidentally use the Time Period ($T$) instead of Frequency ($f$) in the formula $v = f \lambda$?

The calculation will be wrong because speed is wavelength divided by time ($v = \lambda / T$). Multiplying wavelength by time period ($v = \lambda T$) has no physical meaning in wave mechanics.

Define 'Wavelength' and state its standard SI unit.

Wavelength is the distance between two consecutive identical points on a wave (e.g., peak to peak). Its standard SI unit is the metre ($m$).

What is the mathematical formula for the Wave Equation?

The formula is $v = f \lambda$, where $v$ is wave speed, $f$ is frequency, and $\lambda$ is wavelength.

How do you calculate the frequency of a wave if you only know its Time Period ($T$)?

You use the reciprocal formula $f = 1/T$. For example, if the time period is 0.5 seconds, the frequency is $1 / 0.5 = 2 Hz$.

What does the unit 'Hertz' ($Hz$) represent in terms of base units?

Hertz represents 'per second' or $s^{-1}$. It indicates how many cycles or events occur in the span of one second.

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3. Waves

The Wave Equation

Summary

The wave equation is a fundamental mathematical relationship that links the speed of a wave to its frequency and wavelength. This universal principle applies to all wave types, including mechanical waves like sound and electromagnetic waves like light, providing a framework for calculating wave properties across different media.

1. Definition & Core Concepts

The Wave Equation defines the relationship between wave speed ( $v$ ), frequency ( $f$ ), and wavelength ( $\lambda$ ). It states that the speed at which energy is transferred through a medium is the product of the number of waves passing a point per second and the length of a single wave cycle.
Wave Speed ( $v$ ): Measured in metres per second ( $m/s$ ), this represents the distance a specific point on the wave (like a crest) travels in a given amount of time.
Frequency ( $f$ ): Measured in Hertz ( $Hz$ ), this is the number of complete wave cycles that pass a fixed point every second. One Hertz is equivalent to one cycle per second ( $1/s$ ).
Wavelength ( $\lambda$ ): Measured in metres ( $m$ ), this is the physical distance between two consecutive corresponding points on a wave, such as from peak to peak or trough to trough.

A formula triangle showing wave speed (v) at the top, with frequency (f) and wavelength (lambda) at the bottom.

2. Underlying Principles

3. Methods & Techniques

4. Key Distinctions

5. Exam Strategy & Tips

6. Common Pitfalls & Misconceptions