CIE A Level Physics复习笔记7.1.3 The Wave Equation

Category: A-level课程, 教材笔记, 福利干货 Date: 2022年8月16日下午2:42

Derivation of v = f λ

Using the definitions of speed, frequency and wavelength, the wave equation v = fλ can be derived
This is an important relationship between three key properties of a wave
The derivation for this is shown below

7.1.1.4-Derivation-of-vf%CE%BB-1

Derivation of v = fλ

Exam Tip

You will be expected to remember all the steps for this derivation (but do not need to write the full definition for each variable). If you are unsure as to where speed = distance/time comes from, make sure to revisit chapter “2. Kinematics”.

The Wave Equation

The wave equation links the speed, frequency and wavelength of a wave
This is relevant for both transverse and longitudinal waves

7.1.1.5-Wave-equation The Wave Equation

The wave equation tells us that for a wave of constant speed:
- As the wavelength increases, the frequency decreases
- As the wavelength decreases, the frequency increases

7.1.1.5-Frequency-and-wavelength The relationship between frequency and wavelength of a wave

Worked Example

The wave in the diagram below has a speed of 340 m s^–1.

WE-Wave-equation-question-image

What is the wavelength of the wave?

Exam Tip

You may also see the wave equation be written as c = fλ where c is the wave speed. However, c is often used to represent a specific speed ー the speed of light ( 3 x 10⁸ ms^-1). Only electromagnetic waves travel at this speed, therefore it’s best practice to use v for any speed that isn’t the speed of light instead.