IGCSEPhysicsEdexcelRevision Notes3. WavesWaves & The Electromagnetic SpectrumThe Wave Equation

The Wave Equation (Edexcel IGCSE Physics)

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The wave equation

  • All waves obey the wave speed equation

    • This is the relationship between the wave speed, frequency and wavelength of a wave

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)

Formula triangle for the wave speed equation

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

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

  • For more information on how to use a formula triangle refer to the revision note on Speed

Frequency & time period

  • Frequency and time period are defined in Describing wave motion

  • The following equation relates time period and frequency:

f space equals space 1 over T

  • Where:

    • f is frequency measured in Hertz (Hz)

    • T is time period, measured in seconds (s)

Worked Example

Visible light has a frequency of about 6 × 1014 Hz.

How long does it take for one complete cycle of visible light to enter our eyes?

 

Answer:

Step 1: List the known values

  • Frequency, f = 6 × 1014 Hz

Step 2: State the relationship between frequency and time period 

  • This question involves quantities of time and frequency, so the equation which relates time period and frequency of a wave is:

T space equals space 1 over f

Step 3: Substitute the known values into the equation and calculate the time period 

T space equals space 1 space divided by space left parenthesis 6 space cross times space 10 to the power of 14 right parenthesis space equals space 1.67 space cross times space 10 to the power of negative 15 end exponent space straight s

  • Therefore, it takes 1.67 × 10-15 s (to 2 decimal places) for one wave of visible light to pass our eyes

Calculations in different contexts

Worked Example

A certain sound wave moves at about 330 m/s and has a time period of 0.0001 seconds.

Calculate:

a) The frequency of the sound wave

b) The wavelength of the sound wave

 

Answer:

Part (a)

Step 1: List the known quantities

  • Time period, T = 0.0001 s

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

T space equals space 1 over f

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

f space equals space 1 over T

f space equals space fraction numerator 1 over denominator 0.0001 end fraction

f space equals space 10 space 000 space Hz space equals space 1 space cross times space 10 to the power of 4 space Hz

 

Part (b)

Step 1: List the known quantities

  • Wave speed, v = 330 m/s

  • Frequency, f = 1 × 104 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 330 over denominator open parentheses 1 space cross times space 10 to the power of 4 close parentheses end fraction

lambda space equals space 0.033 space straight m

Worked Example

A local radio station broadcasts at a frequency of 200 kHz. The wavelength of these radio waves is 1500 m.

Calculate the speed of these radio waves and state an appropriate unit.

 

Answer:

Step 1: List the known quantities

  • Frequency, f = 200 kHz = 200 000 Hz

  • Wavelength, λ = 1500 m

Step 2: Write out the wave speed equation

  • This question requires wave speed, so state the equation linking wave speed, wavelength and frequency:

v space equals space f space cross times space lambda

Step 3: Substitute the known values to calculate the wave speed 

v space equals space 200 space 000 space cross times space 1500

v space equals space 300 space 000 space 000 space equals space 3 space cross times space 10 to the power of 8 space

Step 4: State the unit with the answer

  • The units for speed are m/s

  • Therefore, the speed of these radio waves is 3 × 108 m/s

Examiner Tips and Tricks

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 state the word equations required

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 the frequency given in kHz: 1 kHz = 1000 Hz

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