AQA A Level Physics復(fù)習(xí)筆記3.1.1 Progressive Waves
Properties of Oscillations
- A progressive wave is defined as:
A wave that transfers energy from one point to another without transferring the medium itself
Properties of a Progressive Wave
- Displacement (x)?of a wave is the distance of a point on the wave from its equilibrium position
- It is a vector quantity; it can be positive or negative
- Amplitude (A)?is the maximum displacement of a particle in the wave from its equilibrium position
- Wavelength (λ)?is the distance between points on successive oscillations of the wave that are in phase
- These are all measured in?metres (m)
Diagram showing the amplitude and wavelength of a wave
- Period (T)?or time period, is the time taken for one complete oscillation or cycle of the wave
- Measured in?seconds (s)
Diagram showing the time period of a wave
- Frequency (f)?is the number of complete oscillations per unit time. Measured in?Hertz?(Hz)?or?s-1
Frequency-period equation
- Speed (v)?is the distance travelled by the wave per unit time
- Measured in?metres per second?(m s-1)
- 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 shows 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 × 108?m s–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.
Phase Difference
- The phase difference between two waves is a measure of?how much a point or a wave is in front or behind another
- This can be found from the relative positive of the crests or troughs of two different waves of the same frequency
- When the crests or troughs are aligned, the waves are?in phase
- When the crest of one wave aligns with the trough of another, they are in?antiphase
- The diagram below shows the green wave?leads?the purple wave by ? λ
Two waves ? λ out of phase
- In contrast, the purple wave is said to?lag?behind the green wave by ? λ
- Phase difference is measured in?fractions of a wavelength, degrees?or?radians
- The phase difference can be calculated from two different points on the same wave or the same point on two different waves
- The phase difference between two points can be described as:
- In phase?is?360o?or 2π radians
- In anti-phase?is?180o?or π radians
Worked Example
Plane waves on the surface of water at a particular instant are represented by the diagram below.
The waves have a frequency of 2.5 Hz.Determine:
a) The amplitude
b) The wavelength
c) The phase difference between points?A?and?B
Exam Tip
When labelling the wavelength and time period on a diagram:
- Make sure that your arrows go from the?very top?of a wave to the very top of the next one
- If your arrow is too short, you will lose marks
- The same goes for labelling amplitude, don’t draw an arrow from the bottom to the top of the wave, this will lose you marks too.
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