Describing Wave Motion & The Wave Equation | Physics for Grade 10 PDF Download

Describing Wave Motion

• When describing wave motion, there are several terms which are important to know, including:
  • Amplitude
  • Wavelength
  • Frequency
  • Period

Amplitude

• Amplitude is defined as:
  The distance from the undisturbed position to the peak or trough of a wave
• It is given the symbol A and is measured in metres (m)
• Amplitude is the maximum or minimum displacement from the undisturbed position

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Wavelength

• Wavelength is defined as
  The distance from one point on the wave to the same point on the next wave.
• In a transverse wave:
  • The wavelength can be measured from one peak to the next peak
• In a longitudinal wave
  • The wavelength can be measured from the centre of one compression to the centre of the next
• The wavelength is given the symbol λ (lambda) and is measured in metres (m)
• The distance along a wave is typically put on the x-axis of a wave diagram

Diagram showing the amplitude and wavelength of a wave

Frequency

• Frequency is defined as:
  The number of waves passing a point in a second
• Frequency is given the symbol f and is measured in Hertz (Hz)

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Time Period

• The time period of a wave is defined as:
  The time taken for a single wave to pass a point 
• This can also be stated as
  The time taken for one full cycle of a wave
• The time period is given the symbol T and is measured in seconds (s)

• On a graph, this can be seen by the time taken for a complete wavelength, if the horizontal axis is time

Diagram showing the time period of a wave

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:

• 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:

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Solved Example

(a) The frequency of the wave
(b) The wavelength of the wave

Part (a)
Step 1: List the known quantities

Time period, T = 2 s
Step 2: Write out the equation relating time period and frequency
T = 1/f
Step 3: Rearrange for frequency, f, and calculate the answer
f = 1 ÷ T = 1 ÷ 2
Frequency, f = 0.5 Hz

Part (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 = 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 = 0.15 ÷ 0.5
Wavelength, λ = 0.30 m

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