IGCSE Physics 0625

3.1 General properties of waves

This section focuses on the fundamental characteristics of waves, with a particular emphasis on the relationship between wave speed, frequency, and wavelength.

Wave Speed, Frequency, and Wavelength

Waves propagate through space by transferring energy. The speed at which this energy travels is known as the wave speed. The frequency is the number of complete wave cycles passing a point per unit time. The wavelength is the distance between two successive crests or troughs of a wave.

The relationship between these three quantities is a fundamental principle in wave physics, expressed by the following equation:

$$v = f \lambda$$

Where:

• v is the wave speed (m/s)
• f is the frequency (Hz)
• λ (lambda) is the wavelength (m)

This equation states that the wave speed is directly proportional to both the frequency and the wavelength. If the frequency increases, the wave speed increases, assuming the wavelength remains constant. Conversely, if the wavelength increases, the wave speed increases, assuming the frequency remains constant.

Understanding the Equation

The equation $v = f \lambda$ is crucial for solving problems involving waves. It allows us to calculate any one of these three quantities if the other two are known. It's important to use consistent units (meters for wavelength, Hertz for frequency, and meters per second for wave speed).

Example Problems

1. Problem: A wave has a frequency of 5 Hz and a wavelength of 2 m. Calculate the wave speed. Solution: Using $v = f \lambda$, we have $v = 5 \text{ Hz} \times 2 \text{ m} = 10 \text{ m/s}$.
2. Problem: A sound wave has a frequency of 440 Hz and travels at a speed of 343 m/s in air. What is its wavelength? Solution: Rearranging the equation to solve for wavelength, we get $\lambda = \frac{v}{f}$. Therefore, $\lambda = \frac{343 \text{ m/s}}{440 \text{ Hz}} \approx 0.78 \text{ m}$.

Wave Speed in Different Mediums

The speed of a wave depends on the medium through which it is traveling. Waves travel at different speeds in different materials. For example, sound travels faster in solids than in liquids, and faster in liquids than in gases. The speed of light is the fastest possible speed in the universe, and it is slower in materials like glass.

Table Summary

Quantity	Symbol	Unit	Definition
Wave Speed	v	m/s	The speed at which a wave propagates through a medium.
Frequency	f	Hz	The number of complete wave cycles passing a point per unit time.
Wavelength	λ	m	The distance between two successive crests or troughs of a wave.