1. Inverse square law

2. P4.5D: Explain how waves propagate from vibrating sources and why the intensity decreases with the square of the distance from a point source
P4.5E: Explain why everyone in a classroom can hear one person speaking, but why an amplification system is often used in the rear of a large concert auditorium.

3. Propagate (scientific definition):
1 : to cause to spread out and affect a greater number or greater area : extend
2 : to transmit (as sound or light) through a medium
Source:

4. How do waves propagate?
Recap
2 types of waves:

5. The inverse square law applies to:
Gravity
Electrostatics
Light (and all electromagnetic waves)
sound

6. The mathematical relationship between the intensity (I) of the source gravity/sound/light, and the intensity measured at distance (d)
I = 1/d2
*this is interchangeable with I = 1/r2 where r= “radius”

7. Why does this occur?
Spray Paint Applet:
As waves propagate in a spherical motion from the source, the energy is spread over a greater area.
Bulb breaking:

8. Balloon Example
Surface of the balloon: wave front radiating out from a wave source – like a loudspeaker.
Depth of color of the balloon: the intensity of the wave.
As the energy (or total available amount of red rubber) has to spread out over a larger and larger area, it gets more thinly spread (sound gets quieter / balloon looks paler).
Applet:

9. Balloon Example
Applet:

10. Gravity Gravity’s strength abides by the inverse square law.
A person at the top of a mountain weighs less than they do at the bottom by a small amount.

11. Light
Like sound, as light leaves its source, the intensity decreases according to the inverse square law.
Video:

12. Example 1: the sun

13. Example 2: Flashlights

15. In addition, the inverse square law applies to all forms of electromagnetic radiation.

16. Q: Why do you think flashlights are designed with a mirror-like surface behind the bulb? Draw a diagram to support your response:

17. Sound
As a sound wave propagates spherically, the sound energy is distributed over the ever-increasing surface diameter of the wave front.
Source:

18. Q: Why does a megaphone make sound project further?

19. A: It increases the amplitude (intensity) of the wave.
The inverse square law is still in effect, but the initial energy is larger, so the wave travels further.