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Amplitude & Intensity (DP IB Physics: SL)

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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

I space proportional to 1 over r squared

  • 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:

Ifraction numerator P over denominator 4 pi space r squared end fraction

  • 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 ∝ 1 over r squared

  • This is an example of an inverse square law relationship

Ix−2

7117-intensity-of-a-spherical-wave

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 

I proportional to A squared

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

Worked example

A person stands 10 m away from a loudspeaker. The sound produced by the loudspeaker is very loud, so the person moves 20 m away from it.

State the effect of this change on the intensity and the amplitude of the sound waves heard by the person.

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 

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Ashika

Author: Ashika

Expertise: Physics Project Lead

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.