Inverse square law
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.
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: http://www.merriam-webster.com/dictionary/propagate
How do waves propagate? Recap 2 types of waves:
The inverse square law applies to: Gravity Electrostatics Light (and all electromagnetic waves) sound
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”
Why does this occur? Spray Paint Applet: http://www.mrwaynesclass.com/teacher/Gravity/InverseSquare/inverse%20square%20law.swf As waves propagate in a spherical motion from the source, the energy is spread over a greater area. Bulb breaking: http://www.acoustics.salford.ac.uk/feschools/waves/bulbvideo.htm
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: http://www.acoustics.salford.ac.uk/feschools/waves/propagation.htm
Balloon Example Applet: http://www.acoustics.salford.ac.uk/feschools/waves/propagation.htm
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.
Light Like sound, as light leaves its source, the intensity decreases according to the inverse square law. Video: https://www.youtube.com/watch?v=F-xNMdIXJIs
Example 1: the sun
Example 2: Flashlights
In addition, the inverse square law applies to all forms of electromagnetic radiation.
Q: Why do you think flashlights are designed with a mirror-like surface behind the bulb? Draw a diagram to support your response:
Sound As a sound wave propagates spherically, the sound energy is distributed over the ever-increasing surface diameter of the wave front. Source: http://www.acousticalsurfaces.com/acoustic_IOI/101_5.htm
Q: Why does a megaphone make sound project further?
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.