The Wave Equation (Edexcel IGCSE Physics: Double Science)
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The Wave Equation
- All waves obey the wave equation, which is used to calculate the wave speed:
- 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:
Frequency & Time Period
- The equation which relates the frequency of a wave to its time period is:
- Where:
- T = time period, measured in seconds (s)
- f = frequency, measured in Hertz (Hz)
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?
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:
Step 3: Substitute the known values in to the equation and calculate the time period
T = 1 ÷ (6 × 1014) = 1.67 × 10-15 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
- The wave equation can be applied and rearranged to calculate properties of waves, such as:
- wave speed
- frequency
- time period
- The wave equation applies to all types of wave, including sound waves and electromagnetic waves
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
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
Step 3: Rearrange for frequency, f, and calculate the answer
f = 1 ÷ T = 1 ÷ 0.0001
Frequency, f = 10 000 Hz = 1 × 104 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 = f × λ
Step 3: Rearrange the equation to calculate the wavelength
λ = v ÷ f
Step 4: Use the frequency you calculated in part (a) and put the values into the equation
λ = 330 ÷ 1 × 104
Wavelength, λ = 0.033 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.
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 = f × λ
Step 3: Substitute the known values to calculate the wave speed
v = 200 000 × 1500 = 300 000 000 = 3 × 108
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
Exam 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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