Stevens' power law facts for kids
Stevens' power law is a scientific idea about how we sense things. It suggests a connection between the actual strength of something physical, like a loud sound or a bright light, and how strong we feel that sensation to be.
Many people believe this law explains a wider range of feelings than an older idea called the Weber-Fechner law. However, some experts question if it is always correct.
The idea is named after a scientist named Stanley Smith Stevens (1906–1973). Even though similar ideas were around in the 1800s, Stevens is famous for bringing this law back. He published a lot of scientific information in 1956 to support it.
How We Sense Things
Imagine you are listening to music. If you turn up the volume a little bit, you might notice a small change in how loud it sounds. But if you turn it up a lot, you might feel a much bigger change in loudness. Stevens' power law tries to explain this. It says that our senses don't always react in a simple, straight line to physical changes.
The Math Behind It
The general way to write this law using math is:
Let's break down what these symbols mean:
is the actual strength of the physical thing. For example, how bright a light is or how much pressure is on your skin.
(pronounced "sigh") is the feeling or sensation you have. This is how strong you feel the light or pressure to be.
is a special number called an "exponent." This number changes depending on what sense we are talking about. For example, the exponent for how loud something sounds is different from the exponent for how bright something looks.
is a starting number that helps make the math work out. It also depends on the type of sensation and the units used to measure it.
Examples of Exponents
The table below shows different "exponents" (the 'a' value) that Stevens found for various sensations. These numbers help us understand how our senses react.
For example:
- For Loudness, the exponent is 0.67. This means if a sound gets much louder physically, we might not feel it as being *that* much louder. Our hearing compresses the range.
- For Electric shock, the exponent is 3.5. This is a high number! It means a small increase in electric current can feel like a very big increase in pain. Our body reacts strongly to protect us.
- For Visual length, the exponent is 1. This means if a line gets twice as long, we usually see it as exactly twice as long. Our eyes are very good at judging length accurately.
| Continuum | Exponent () |
Stimulus condition |
|---|---|---|
| Loudness | 0.67 | Sound pressure of 3000 Hz tone |
| Vibration | 0.95 | Amplitude of 60 Hz on finger |
| Vibration | 0.6 | Amplitude of 250 Hz on finger |
| Brightness | 0.33 | 5° target in dark |
| Brightness | 0.5 | Point source |
| Brightness | 0.5 | Brief flash |
| Brightness | 1 | Point source briefly flashed |
| Lightness | 1.2 | Reflectance of gray papers |
| Visual length | 1 | Projected line |
| Visual area | 0.7 | Projected square |
| Redness (saturation) | 1.7 | Red-gray mixture |
| Taste | 1.3 | Sucrose |
| Taste | 1.4 | Salt |
| Taste | 0.8 | Saccharine |
| Smell | 0.6 | Heptane |
| Cold | 1 | Metal contact on arm |
| Warmth | 1.6 | Metal contact on arm |
| Warmth | 1.3 | Irradiation of skin, small area |
| Warmth | 0.7 | Irradiation of skin, large area |
| Discomfort, cold | 1.7 | Whole body irradiation |
| Discomfort, warm | 0.7 | Whole body irradiation |
| Thermal pain | 1 | Radiant heat on skin |
| Tactual roughness | 1.5 | Rubbing emery cloths |
| Tactual hardness | 0.8 | Squeezing rubber |
| Finger span | 1.3 | Thickness of blocks |
| Pressure on palm | 1.1 | Static force on skin |
| Muscle force | 1.7 | Static contractions |
| Heaviness | 1.45 | Lifted weights |
| Viscosity | 0.42 | Stirring silicone fluids |
| Electric shock | 3.5 | Current through fingers |
| Vocal effort | 1.1 | Vocal sound pressure |
| Angular acceleration | 1.4 | 5 s rotation |
| Duration | 1.1 | White noise stimuli |
it:Soglia percettiva
See also
In Spanish: Función potencial de Stevens para niños
