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GCSEPhysicsWJECRevision Notes1. Electricity, Energy & Waves1.5 Features of WavesWave Equations

Wave Equations (WJEC GCSE Physics)

Revision Note

Caroline

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Caroline

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Wave Equations

  • Wave speed is defined as:

The distance travelled by a wave each second

  • The wave speed can be calculated in a similar way to calculating the speed of moving objects:

wave space speed space equals space distance over time

  • Where:
    • Wave speed is measured in metres per second (m/s)
    • Distance travelled by the wave is measured in metres (m)
    • Time taken is measured in seconds (s)

  • All waves obey the wave equation, which is another way to calculate the wave speed:

table attributes columnalign right center left columnspacing 0px 0px 0px end attributes row cell wave space speed space end cell equals cell space wavelength space cross times space frequency end cell end table

table row cell nu space end cell equals cell space f space lambda end cell end table

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

  • Higher tier students may need to rearrange the wave equation, which can be done using a formula triangle

Formula Triangle Relating Wave Speed, Frequency and Wavelength

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

A formula triangle can be used to help rearrange the wave equation

Worked example

Sound waves in air travel with a frequency of 170 Hz and a wavelength of 2 m. Calculate the speed of sound waves in air.

Answer:

Step 1: List the known quantities

  • Frequency, f = 170 Hz
  • Wavelength, lambda,  = 2 m

Step 2: Write out the wave equation

nu space equals space f space lambda

Step 3: Substitute the known quantities into the wave equation  to calculate wave speed

table row cell nu space end cell equals cell space 170 space cross times space 2 end cell row blank blank blank row cell nu space end cell equals cell space 340 space straight m divided by straight s end cell end table

Worked example

Higher Tier

A wave in a pond has a speed of 0.15 m/s and a frequency of 0.5 Hz. Calculate the wavelength of the wave.

Answer:

Step 1: List the known quantities

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

Step 2: Write out the wave equation

nu space equals space f space lambda

Step 3: Substitute the known quantities into the wave equation 

0.15 space equals space 0.5 space cross times space lambda

Step 4: Rearrange to calculate the wavelength

table row cell lambda space end cell equals cell space fraction numerator 0.15 over denominator 0.5 end fraction end cell row blank blank blank row cell lambda space end cell equals cell space 0.30 space straight m end cell end table

Examiner Tip

When stating equations make sure you use the right letters:

  • For example, use lambda 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 sometimes wavelength may be given in other units, such as cm or km. When calculating wave speed, check what units for speed the question requires and be prepared to convert the wavelength accordingly.
  • Likewise, watch out for frequency given in kHz: 1 kHz = 1000 Hz

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    Caroline

    Author: Caroline

    Expertise: Physics Lead

    Caroline graduated from the University of Nottingham with a degree in Chemistry and Molecular Physics. She spent several years working as an Industrial Chemist in the automotive industry before retraining to teach. Caroline has over 12 years of experience teaching GCSE and A-level chemistry and physics. She is passionate about creating high-quality resources to help students achieve their full potential.