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### Course: Health and medicine > Unit 8

Lesson 5: Sensory perception# Weber's law and thresholds

Weber's law explains how we perceive changes in stimuli like weight or sound. It states that the ratio of the smallest noticeable change in a stimulus (delta I) to the original intensity of the stimulus (I) is a constant (K). This relationship predicts a linear increase in the noticeable difference as the intensity of the stimulus increases.
Created by Ronald Sahyouni.

## Want to join the conversation?

- What does the Weber's law and threshold have to do with sensory perception? or the nervous system(5 votes)
- Sensation is proportional to the logarithm of the stimulus intensity.(10 votes)

- When he explains the equation at5:50, isn't the explanation backwards? Shouldn't the Weber

fraction be the incremental threshold over the background intensity?(5 votes)- He gave the correct equation in5:05, he just made an error when reexplaining in6:02.(4 votes)

- What are the exact threshold percentages in determining weight differences? Sound differences? Temperature difference?(4 votes)
- I think it is a relative threshold, if you are lifting 500 KG and you add 70 grams you might not notice it. And when you are lifting a wedding ring which weighs 20 grams, and you add 70 grams to it - you will notice it. The same hold true for light brightness and sound.

"Weber's Law states that the ratio of the increment threshold to the background intensity is a constant. So when you are in a noisy environment you must shout to be heard while a whisper works in a quiet room. And when you measure increment thresholds on various intensity backgrounds, the thresholds increase in proportion to the background." - The quote source : http://www.cis.rit.edu/people/faculty/montag/vandplite/pages/chap_3/ch3p1.html

I think the percentage is relative to where you measure it. And I know there is a mathematical equation for it, which I linked in here, but no actual fixed percentage, or one that scales for all.(2 votes)

- In class, when it comes to Weber's Law, my teacher says, "We perceive differences on a logarithmic, not a linear scale." (or something like that) What does it mean? I mean, how does it have to do with the linear graph at7:26since my teacher uses the word "logarithmic"?(3 votes)
- All it means is that, the relation between our perceived differences in the stimuli, and that between the energies of those stimuli is logarithmic. For some sensations (like sound), by increasing the stimuli 10 times (from a 100 to a thousand), you would perceive the change of 10 decibels rather than 900 as you would otherwise expect. Here the power is 1, but it can be varied, such that a 10 times increase would produce say square-root(10) times change in the perceived sensation.(1 vote)

- Did you misspeak at6:00? I think you have the ratio of the incremental threshold to the background intensity written, but you said it the other way around.

Also, are the JND and incremental threshold the same?(1 vote)- Sorry for being extremely late, but for those who will see this in the future, yes JND and incremental threshold are the SAME.(3 votes)

- Hello, what would be an example of "baseline stimuli" that would need to be surpassed when trying calculate "K" in real world situations?

I kind of inferred that "a" in ∆I/ a+ I = K , could be gravity if we are looking at it in the context of lifting a weight. Or even air when looking at it in the context of sound/hearing something.

Please let me know if this is a correct understanding.

Thank you!(2 votes) - 3:30The sensory neurons that Ronald mentions, are they afferent neurons?

Also, what kind of receptor is being used (i.e. position or touch mechanoreceptors)?(1 vote) - How is Fechner's law different than Webber's Law?(1 vote)
- Actually, Fechner was the other individual who helped characterize the "law" that you saw in this video. The "Fechner's law" or "Weber's law" is actually called the "Weber-Fechner law".(2 votes)

- What's the difference between Weber's law and Fechner's law?(1 vote)
- At8:12, its noted that weber's law is a good rule of thumb. For the MCAT should we accept applying weber's law for all stimulus or are there certain exceptions we should note?(1 vote)

## Video transcript

Voiceover: Imagine that
we've got your arm here, and you got these nice big strong muscles, and you're holding in your hand a weight. Let's say that you're
holding a two-pound weight. Here is a two-pound weight. Let's say that you are
holding it in your hand and you want to lift it up. As you lift this two-pound weight, you notice that there is some resistance, and you definitely are able to notice that there is a weight in your hand. Let's say that we took this weight and you didn't know, let's say I grabbed the
weight out of your hand and I replaced it with another weight that was 2.05 pounds. I've got this 2.05-pound weight, and it's the same exact
shape and everything, and it's just .05 pounds heavier. Let's say that we replaced this guy with the 2.05-pound weight. Let's say that I asked you to lift this new 2.05-pound weight, and you might lift it, and you may notice that it's different, but most people in general would not notice any difference. They would just think it's the
same exact two-pound weight. Basically, what I'm trying to say is that this .05-pound
increase in the weight, for most people probably, would not be noticeable. Let's say that instead of
giving you a 2.05-pound weight let's say that I gave you a weight that was 2.2 pounds, and let's say you close your eyes and I took this two-pound
weight out of your hand, and I replaced it with
this new 2.2-pound weight, and then I ask you to lift the new weight. Most people would probably
notice this new increase, this new weight. Basically, what I'm trying to say is that a addition of .05 pounds
probably wouldn't get noticed, whereas an addition of 0.2
pounds would get noticed. The threshold at which
you're able to notice an increase or a change in weight or really any sensation so that threshold, where
you go from not noticing a tiny little change to actually noticing a tiny little change is known as the just
noticeable difference, noticeable difference. We can abbreviate this as JNT. In this case, the just
noticeable difference, let's say for just sake of argument, is .2 pounds, .2 pounds. OK. Let's imagine that instead of starting with a two-pound weight, instead, we started with
a five-pound weight, so five-pound weight. The five-pound weight is much heavier than the two-pound weight. In this case, if I replace the five-pound weight with a 5.2-pound weight, because it's a lot heavier and you're using a lot more muscle fibers in order to lift the five-pound weight, you may not notice the .2-pound increase. Whereas if I replaced
the five-pound weight with a 5-1/2-pound weight, so 5.5-pound weight, and I asked you to lift it, you might notice the
half a pound increase, but you might not notice
the .2-pound increase. Basically, what's going on here is that since you're using more muscle fibers, you're using more sensory neurons, they're not as sensitive
to small increases. They're not as sensitive
to the 0.2-pound increase. You need a bigger just
noticeable difference in order to actually be mentally aware of the change in weight. Basically, when you're
holding five pounds, let's say for sake of argument, the just noticeable difference
is a little bit higher than when you're holding two pounds. Now, these numbers we're
just throwing around, and if you actually did
this experimentally, the actual numbers might be different, but the concept generally
would remain the same. In the five-pound weight category, the just noticeable
difference is .5 pounds. From this, we can come
up with an equation. Let's just define some variables. I, or the intensity of the stimulus, is equal to two pounds in this case and five pounds in this case. And delta I, so delta I, would be the just noticeable difference. It would be 5.5 pounds minus five pounds equals half a pound. For the five-pound example, I would be five, and delta I would be .5, and then in the two-pound example, I would be two, and delta I would be .2. Basically, there is actually
a guy back in the day named Weber. Weber noticed in 1834 that the ratio of the increment threshold, the ratio of the increment threshold, which is this over here, to the background intensity, which is this over here, so this is the background intensity, is constant. If we were to take .2 divided by two, and if we were to take .5 divided by five, this ratio is actually equal, and it equals .1, and this ratio would be
more or less fairly constant for a bunch of different weights. That's what Weber's law is. Weber, in 1834, realized that
there is this relationship. We can write this as an equation. Delta I over I equals K. K is a constant for
each individual person. There is this particular threshold, and the ratio, the background intensity to
the incremental threshold is relatively constant, and that constant is this K value. This part of the equation over here is known as the Weber fraction. This works for sensory tactile
stimuli like lifting a weight but it also works for auditory stimuli. Imagine you're in a quiet room. If you're in a quiet
room with someone else, you can whisper. You can talk really, really softly and the person can hear you. But if you're at a rock concert, you have to be yelling
at the top of your lungs in order for someone
next to you to hear you. That's because the background intensity in a quiet room versus a concert is different, and so the delta I, which is whether you're just whispering or whether you're yelling, is different in accordance
with the background intensity. That's what the Weber's
law is basically saying. If we take this equation over here, let me just give myself
a little bit of space. If we take this equation, Weber's law, and rearrange it, so we have delta I equals
the background intensity times this constant, if we arrange it, we can see that this Weber's law predicts a linear relationship between
the incremental threshold, which is this value over here, and the background intensity. In other words, as the
background intensity gets bigger, the incremental threshold gets bigger. If we were to draw a little graph, if we were to draw a
graph where the x-axis is the background intensity and the y-axis was the incremental, the difference threshold, what we would see would be
this linear relationship. Using the concert example over here, a really, really big background intensity would result in a delta I, so this would be ... Let's say delta I in this case was how loud you were talking. The delta I would have to be a lot bigger than if you were in a quiet room, so quiet room. This law would generally hold true for almost any type of stimulus. It's a good rule of thumb. It's not exactly set in stone, but it is kind of how most of your different sensations operate, where if there is a bigger
background intensity, you need a bigger difference threshold in order to actually
perceive the sensation. In the real world, sometimes people add a different value. You got delta I over I equals K. This is the normal Weber's law. Some people will even add in
another constant over here in order to take into account the baseline level of activity that needs to be surpassed
in real-world situations. So this equation can be modified in order to more accurately
represent what goes on in the real world.