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

• 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?