4.3.2 Amplitude & Intensity

Intensity

• The intensity of a wave is defined as follows:

Power per unit area 

• Intensity is measured in W m^–2

• Power is defined as:

The rate of energy transfer

• Therefore, intensity can also be defined as:

The rate of energy transfer per unit area

• For spherical waves being emitted by a point source equally in all directions, the intensity follows an inverse square law with distance from the point source

• Where:
  • I = intensity of the wave in watts per metre squared (W m^–2)
  • r = distance from the point source in metres (m)

• For spherical waves being emitted by a point source equally in all directions, the intensity at the surface of a sphere is calculated using:

I = 

• Where:
  • P = power in watts (W)
  • r = radius of sphere in metres (m)
• For spherical waves being emitted by a point source equally in all directions, the power is a constant, therefore the relationship can be expressed as:

I ∝ 

• This is an example of an inverse square law relationship

I ∝ x⁻²

Intensity decreases by the inverse square law

Intensity Variation with Amplitude

• By definition, the intensity of a wave (its power per unit area) is proportional to the energy transferred by the wave
• The intensity of a wave at a particular point is related to the amplitude of the wave at that point
• The energy transferred by a wave is proportional to the square of the amplitude
• Therefore, the intensity of a wave is proportional to the square of the amplitude 

• Where:
  • I = intensity of the wave in W m^–2
  • A = amplitude of the wave in metres (m)

Step 1: Write down the known quantities

• • Original distance, r₁ = 10 m
  • New distance, r₂ = 20 m

Step 2: Write down the relationship between the intensity of a wave and the distance from the point source producing the wave 

Step 2: State the new intensity

• • Since the distance doubles (r₂ = 2r₁), the intensity is reduced by a factor four 

Step 3: Write down the relationship between the intensity of a wave and its amplitude 

Step 4: State the new amplitude

• • Since the intensity is reduced by a factor four, the amplitude decreases by half