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Stevens' power law facts for kids

Kids Encyclopedia Facts

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:

\psi(I) = k I ^a , \,\!

Let's break down what these symbols mean:

  • I is the actual strength of the physical thing. For example, how bright a light is or how much pressure is on your skin.
  • \psi (pronounced "sigh") is the feeling or sensation you have. This is how strong you feel the light or pressure to be.
  • a 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.
  • k 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 (a) 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

Kids robot.svg In Spanish: Función potencial de Stevens para niños

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