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Properties of Waves (HL IB Physics)

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Ashika

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Ashika

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Properties of Waves

  • Travelling waves are defined as follows:

Oscillations that transfer energy from one place to another without transferring matter

  • Waves transfer energy, not matter
  • Waves are generated by oscillating sources 
    • These oscillations travel away from the source
  • Oscillations can propagate through a medium (e.g. air, water) or in vacuum (i.e. no particles), depending on the type of wave

  • The key properties of travelling waves are as follows:

Displacement

  • 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
    • Measured in metres (m)

Wavelength

  • Wavelength λ is the length of one complete oscillation measured from the same point on two consecutive waves 
    • For example, two crests, or two troughs
    • Measured in metres (m)

Amplitude

  • Amplitude A is the maximum displacement of an oscillating wave from its equilibrium position (x = 0)
    • Amplitude can be positive or negative depending on the direction of the displacement 
    • Measured in metres (m)
    • Where the wave has 0 amplitude (the horizontal line) is referred to as the equilibrium position

Amplitude and wavelength

Diagram showing the amplitude and wavelength of a wave

Period & Frequency

  • Period (T) is the time taken for a complete oscillation to pass a fixed point
    • Measured in seconds (s)
  • Frequency (f) is the number of complete oscillations to pass a fixed point per second
    • Measured in Hertz (Hz)
  • The frequency, f, and the period, T, of a travelling wave are related to each other by the equation:

f space equals space fraction numerator space 1 over denominator T end fraction

  • Where:
    • f = frequency (Hz)
    • T = time period (s)

4-2-1-period-and-frequency_sl-physics-rn

Period T and frequency f of a travelling wave

Wave speed

  • Wave speed (v) is the distance travelled by the wave per unit time
    • Measured in metres per second (m s-1)
  • The wave speed is defined by the equation:

v space equals space f lambda space equals space fraction numerator space lambda over denominator T end fraction

  • Where:
    • v = wave speed (m s–1)
    • λ = wavelength (m)

  • This is referred to as the wave equation
  • It tells us that for a wave of constant speed:
    • As the wavelength increases, the frequency decreases
    • As the wavelength decreases, the frequency increases

 Frequency and wavelength, downloadable AS & A Level Physics revision notes

The relationship between the frequency and wavelength of a wave

Worked example

The graph below shows a travelling wave.

4-2-1-we-properties-of-wave-question-graphDetermine:

(a) The amplitude A of the wave, in m.

(b) The frequency f of the wave, in Hz.

Answer:

(a) Identify the amplitude A of the wave on the graph 

  • The amplitude is defined as the maximum displacement from the equilibrium position (x = 0)
4-2-1-we-properties-of-wave-step-1
  • The amplitude must be converted from centimetres (cm) into metres (m)

A = 0.1 m

(b) Calculate the frequency of the wave

Step 1: Identify the period T of the wave on the graph 

  • The period is defined as the time taken for one complete oscillation to occur


4-2-1-we-properties-of-wave-step-2

  • The period must be converted from milliseconds (ms) into seconds (s)

T = 1 × 10–3 s

Step 2: Write down the relationship between the frequency f and the period T 

f space equals space fraction numerator space 1 over denominator T end fraction

Step 3: Substitute the value of the period determined in Step 1

f space equals space fraction numerator 1 over denominator 1 space cross times space 10 to the power of negative 3 end exponent end fraction space equals space 1000 space Hz

Worked example

The wave in the diagram below has a speed of 340 m s–1.WE - Wave equation question image, downloadable AS & A Level Physics revision notes

Determine the wavelength of the wave.

Answer:

Worked example - wave equation, downloadable AS & A Level Physics revision notes

 

Worked example

A travelling wave has a period of 1.0 μs and travels at a velocity of 100 cm s–1.

Calculate the wavelength of the wave, in m.

Answer:

Step 1: Write down the known quantities

  • Period, T = 1.0 μs = 1.0 × 10–6 s
  • Velocity, v = 100 cm s–1 = 1.0 m s–1

Note the conversions:

    • The period must be converted from microseconds (μs) into seconds (s)
    • The velocity must be converted from cm s–1 into m s–1

Step 2: Write down the relationship between the frequency f and the period T 

f space equals space 1 over T

Step 3: Substitute the value of the period into the above equation to calculate the frequency 

f space equals space fraction numerator 1 over denominator 1 space cross times space 10 to the power of negative 6 end exponent end fraction space equals space 1 space cross times space 10 to the power of 6

Step 4: Write down the wave equation

v space equals space f lambda

Step 5: Rearrange the wave equation to calculate the wavelength λ

lambda space equals space fraction numerator space f over denominator v end fraction

Step 6: Substitute the numbers into the above equation 

lambda space equals space fraction numerator 1 over denominator 1 space cross times space 10 to the power of 6 end fraction space equals space 1 space cross times space 10 to the power of negative 6 end exponent

Examiner Tip

You must be able to interpret different properties of waves from a variety of graphs. You may recognise calculating the time period and wavelength look very similar (the distance for one full wave). This is the time period if the x-axis is time. If the x-axis is distance, then this distance is the wavelength.

Pay very close attention to units. If you want a frequency in Hertz, then the time period must be in seconds and not milliseconds etc.  

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    Ashika

    Author: Ashika

    Expertise: Physics Project Lead

    Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.