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O LevelPhysicsCambridgeRevision Notes3. Waves3.1 General Properties of WavesThe Wave Equation

The Wave Equation (Cambridge O Level Physics)

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Dan MG

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Dan MG

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The Wave Equation

  • Wave speed is defined as:

The distance travelled by a wave each second

  • Wave speed is given the symbol ν and is measured in metres per second (m/s)
  • Wave speed is the speed at which energy is transferred through a medium
  • Transverse and longitudinal waves both obey the wave equation:

v space equals space f space cross times space lambda

  • Where:
    • v = wave speed in metres per second (m/s)
    • f = frequency in hertz (Hz)
    • λ = wavelength in metres (m)

  • The wave speed equation may need to be rearranged, which can be done using this formula triangle:

Equation Triangle for the Wave Equation

Wave speed triangle (2), IGCSE & GCSE Physics revision notes

Worked example

A wave in a pond has a speed of 0.15 m/s and a time period of 2 seconds. Calculate:

a) The frequency of the wave

b) The wavelength of the wave

Answer:

(a)

Step 1: List the known quantities

  • Time period, T = 2 s

Step 2: Write out the equation relating time period and frequency

f space equals space 1 over T

Step 3: Rearrange for frequency, f, and calculate the answer

f space equals space 1 half

Frequency, f = 0.5 Hz

(b)

Step 1: List the known quantities

  • Wave speed, v = 0.15 m/s
  • Frequency, f = 0.5 Hz

Step 2: Write out the wave speed equation

v space equals space f space cross times space lambda

Step 3: Rearrange the equation to calculate the wavelength

lambda space equals space v over f

Step 4: Use the frequency you calculated in part (a) and put the values into the equation

lambda space equals space fraction numerator 0.15 over denominator 0.5 end fraction

Wavelength, λ = 0.30 m

Examiner Tip

When stating equations make sure you use the right letters:

For example, use λ for wavelength, not L or W

If you can’t remember the correct letters, then just state the word equations

Be careful with units: wavelength is usually measured in metres and speed in m/s, but if the wavelength is given in cm you might have to give the speed in cm/s

Likewise, watch out for frequency given in kHz: 1 kHz = 1000 Hz

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    Dan MG

    Author: Dan MG

    Expertise: Physics

    Dan graduated with a First-class Masters degree in Physics at Durham University, specialising in cell membrane biophysics. After being awarded an Institute of Physics Teacher Training Scholarship, Dan taught physics in secondary schools in the North of England before moving to SME. Here, he carries on his passion for writing enjoyable physics questions and helping young people to love physics.