Wavelength varies inversely with frequency.
Let [tex]$x=$[/tex] wavelength and [tex]$y=$[/tex] frequency.
Visible Light
Wavelength (m)
Frequency (THz)
[tex]$k$[/tex]
Blue
450
670
301,500
Green
520
580
301,600
Yellow
560
540
302,400
Red
635
480
304,800
The equation that models the relationship between the wavelength and frequency of yellow light is:
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Answer (2)
The problem states that wavelength and frequency are inversely proportional, meaning x y = k .
For yellow light, the wavelength is 560 m and the frequency is 540 THz.
Calculate the constant of proportionality: k = 560 × 540 = 302400 .
The equation that models the relationship is x y = 302400 .
Explanation
Understanding the Inverse Relationship We are given that wavelength ( x ) varies inversely with frequency ( y ). This means that their product is a constant, i.e., x y = k , where k is a constant. We are given a table of values for different colors of light, and we want to find the equation that models the relationship between wavelength and frequency for yellow light.
Finding the Constant of Proportionality From the table, for yellow light, the wavelength x = 560 m and the frequency y = 540 THz. We can find the constant k by multiplying these values: k = x y = 560 × 540 .
Determining the Equation Calculating the value of k , we have k = 560 × 540 = 302400 . Therefore, the equation that models the relationship between the wavelength and frequency of yellow light is x y = 302400 .
Examples
Understanding inverse relationships is crucial in many fields. For example, in economics, the price of a product often has an inverse relationship with demand: as the price increases, the demand typically decreases. Similarly, in physics, the speed of a vehicle and the time it takes to travel a certain distance are inversely related: the faster the speed, the less time it takes. Recognizing and modeling these relationships helps in making informed decisions and predictions.
The equation that models the relationship between the wavelength and frequency of yellow light is x y = 302400 . This reflects the inverse relationship between wavelength and frequency, where their product remains constant. Thus, as one value increases, the other decreases proportionally.
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