Intensity is defined as the power passing through a surface per unit area. Intensity and distance have an inverse square relationship. Intensity is proportional to the square of the amplitude of the wave.
Equations
Description
Symbol Equation
Intensity of radiation equation
I=AP
Intensity at surface of sphere equation
I=4πr2P
Inverse square law
I∝r21
Intensity-amplitude relationship
I∝(amplitude)2
Variable definitions
Quantity name
Symbol
Derived Unit
Alternate unit
Si Unit
intensity
I
Wm−2
Js−1m−2
kgs−3
power
P
W
Js−1
kgm2s−3
area
A
m2
m2
distance
r
m
m
amplitude
A
m
m
Intensity
Intensity is the power passing through a surface per unit area. The units of intensity are watts per square metre (Wm−2).
I=AP
A progressive wave spreads out as the distance from the source increases. The energy and power transferred by the wave is also spread out over this increasing area.
Example
A torch light used at night doesn't carry on going all the way into space. The light gets dimmer and spreads out as the distance from the torch increases.
Intensity and distance
A spherical wave is emitted from a point source and spreads out equally in every direction.
1.
Point source emitting spherical waves
2.
Surface area of a sphere, A=4πr2
The power and energy radiated by the source spreads out over the surface of the sphere. The surface area of the sphere increases as the distance from the source increases. This means the same power is spread over a larger area.
This means that at a distance r from the source, the total power P is spread over the surface area of the sphere A. The surface area of a sphere is 4πr2. This gives a new equation for intensity.
I=4πr2P
From this equation it can be seen that there is an inverse square relationship between intensity I and the distance from the source r. This is called the inverse square law.
I∝r21
Example
The total power output of the Sun is 3.8×1026W. The intensity of the radiation measured on Mars is 590Wm−2. Calculate the distance between the Sun and Mars. Give your answer in km.
First, write out the quantities given by the question and check they are in the correct form:
P=3.8×1026WI=590Wm−2
Next, write out the equation needed:
I=4πr2Pr=4πIP
Then, substitute the values into the equation:
r=4π×5903.8×1026=2.2639...×1011
Make sure to include the correct units and round to the lowest number of significant figures of the values given:
r=2.3×1011m=10002.3×1011=2.3×108km
ThedistancebetweentheSunandMarsis2.3×108km.
Investigating the inverse square law
A light dependent resistor (LDR) can be used to investigate the inverse square law. A lamp can be used as the light source.
An LDR decreases in resistance as the intensity detected decreases. Each LDR has a calibration curve that can be used to match the resistance measured to the intensity of the light.
This can be plotted graphically.
Example
Intensity and amplitude
As the energy of a wave spreads out, the amplitude of the wave decreases.
The amplitude of the wave is proportional to the average speed of the oscillating particles. Decreasing the amplitude means decreasing this speed and therefore decrease the kinetic energy of the particles (Ek=21mv2).
Kinetic energy is proportional to the square of the speed and therefore the square of the amplitude. This means that intensity is proportional to the square to the amplitude.
I∝(amplitude)2
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Waves: properties, types and equations
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Intensity of a wave
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FAQs - Frequently Asked Questions
How can the inverse square law be investigated?
A light dependent resistor (LDR) can be used to investigate the inverse square law. A lamp can be used as the light source.
Is intensity the same as amplitude?
Intensity is proportional to the square of the amplitude of the wave.
What is wave intensity?
Intensity is defined as the power passing through a surface per unit area.