CIE A Level Physics复习笔记7.1.3 The Wave Equation
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
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
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
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.
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.
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