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The Weber-Fechner law states that the magnitude of a perceived sensation increases as log10 of stimulus intensity. Let us assume a background stimulus level of 1 unit, which increases to 10 units in situation P and to 100 units in situation Q. The perceived sensation in situation Q is stronger than the sensation perceived in situation P by a factor of ______. (Use decimal notation, not fractions or percentage)
Correct answer is between '1.9,2.1'. Can you explain this answer?
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The Weber-Fechner law states that the magnitude of a perceived sensati...
The Weber-Fechner law describes the relationship between the magnitude of a perceived sensation and the intensity of a stimulus. According to this law, the perceived sensation increases as the logarithm (base 10) of the stimulus intensity increases.
In this scenario, we are given a background stimulus level of 1 unit, which increases to 10 units in situation P and to 100 units in situation Q. We need to determine the factor by which the perceived sensation in situation Q is stronger than the sensation perceived in situation P.
To calculate this factor, we need to find the logarithm (base 10) of the stimulus intensity in each situation.
1. Logarithm of stimulus intensity in situation P:
log10(10) = 1
2. Logarithm of stimulus intensity in situation Q:
log10(100) = 2
Now, we can compare the logarithms to find the factor by which the perceived sensation in situation Q is stronger than in situation P.
The perceived sensation in situation Q is stronger by a factor of:
2 - 1 = 1
However, the question asks for the factor in decimal notation, not as a whole number. To convert the factor to decimal notation, we can consider that each whole number represents a factor of 10.
Since 1 represents a factor of 10, we can say that the factor in decimal notation is between 1.0 and 1.9.
To further narrow down the range, we can consider that the next whole number, 2, represents a factor of 100. Therefore, the factor in decimal notation is between 1.9 and 2.1.
Hence, the correct answer is between 1.9 and 2.1.
In this scenario, we are given a background stimulus level of 1 unit, which increases to 10 units in situation P and to 100 units in situation Q. We need to determine the factor by which the perceived sensation in situation Q is stronger than the sensation perceived in situation P.
To calculate this factor, we need to find the logarithm (base 10) of the stimulus intensity in each situation.
1. Logarithm of stimulus intensity in situation P:
log10(10) = 1
2. Logarithm of stimulus intensity in situation Q:
log10(100) = 2
Now, we can compare the logarithms to find the factor by which the perceived sensation in situation Q is stronger than in situation P.
The perceived sensation in situation Q is stronger by a factor of:
2 - 1 = 1
However, the question asks for the factor in decimal notation, not as a whole number. To convert the factor to decimal notation, we can consider that each whole number represents a factor of 10.
Since 1 represents a factor of 10, we can say that the factor in decimal notation is between 1.0 and 1.9.
To further narrow down the range, we can consider that the next whole number, 2, represents a factor of 100. Therefore, the factor in decimal notation is between 1.9 and 2.1.
Hence, the correct answer is between 1.9 and 2.1.
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The Weber-Fechner law states that the magnitude of a perceived sensation increases as log10 ofstimulus intensity. Let us assume a background stimulus level of 1 unit, which increases to 10 unitsin situation P and to 100 units in situation Q. The perceived sensation in situation Q is stronger thanthe sensation perceived in situation P by a factor of ______. (Use decimal notation, not fractions orpercentage)Correct answer is between '1.9,2.1'. Can you explain this answer?
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