# PHY C14: Energy & Intensity of Waves

We’re covering:

• Intensity
• Relationship between Intensity & Amplitude

Let’s go!

We saw that waves transfer ENERGY as they propagate.

Now we will look at waves which propagate from a point source.

The waves propagate away from the point source & cover an area around the source.
Since waves travel in 3D, the area is a SPHERE.

What is intensity?
Amount of energy transferred per unit surface area per unit time.

Intensity = energy transferred ÷ surface area of sphere ÷ time
I = E/(4πr2 x t)

Since energy/time = power, intensity is POWER over SURFACE AREA.
I = P/(4πr2)

Remember:
Intensity = power given out to a surface area of a sphere of SPACE surrounding the POINT SOURCE:

But you can calculate the power given to an OBJECT at a certain distance from the point source by
MULTIPLYING the intensity by the exposed surface area of the object:
P transferred to object = I x Surface Area of Object
P transferred to object = P/(4πr2) x Surface Area of Object

How is intensity related to amplitude?
Energy is proportional to the square of the amplitude:
E ∝ A2
E = kA2

Thus, power follows the same relationship (if time is unchanged):
P ∝ A2
P = kA2

Thus, the same goes for intensity:
Intensity is proportional to the square of the amplitude.
I ∝ A2
I = kA2

*The constant (k) is NOT the same for all 3 relationships.
Since time & surface area are constant in these situations, k includes these factors.

This proportionality constant (k) also differs for different waves in different situations.
It can be determined experimentally (by drawing a graph).

⇐ Previous in Physics: Wave Motion
⇒ Next in Physics: Transverse & Longitudinal Waves