Wavelength varies inversely with frequency. Let [tex]$k$[/tex] be the product of wavelength and frequency. Complete the table using the inverse variation relationship.
| Visible Light | Wavelength (m) | Frequency (THz) | [tex]$k$[/tex] |
| :------------ | :------------- | :-------------- | :---------- |
| Blue | 450 | [tex]$a$[/tex] | 301,500 |
| Green | 520 | 580 | [tex]$b$[/tex] |
| Yellow | [tex]$c$[/tex] | 540 | 302,400 |
| Red | 635 | 480 | 304,800 |
[tex]$a=\square$[/tex] [tex]$b=301, \square$[/tex] [tex]$c=\square$[/tex]
Answer (2)
Calculate b using the values for Green light: b = 520 × 580 = 301600 .
Calculate a using the values for Blue light: a = 450 301500 = 670 .
Calculate c using the values for Yellow light: c = 540 302400 = 560 .
The missing values are a = 670 , b = 301600 , and c = 560 , so the final answer is a = 670 , b = 301600 , c = 560 .
Explanation
Understanding the Problem We are given a table relating the wavelength and frequency of different colors of visible light. We know that wavelength and frequency are inversely proportional, meaning their product is a constant, k . We need to find the missing values a , b , and c in the table.
Calculating b First, let's find the value of b . We know that for Green light, the wavelength is 520 m and the frequency is 580 THz. Since k is the product of wavelength and frequency, we have: b = 520 × 580 = 301600
Calculating a Next, let's find the value of a . We know that for Blue light, the wavelength is 450 m and k = 301 , 500 . Since k is the product of wavelength and frequency, we have: a = 450 301500 = 670
Calculating c Finally, let's find the value of c . We know that for Yellow light, the frequency is 540 THz and k = 302 , 400 . Since k is the product of wavelength and frequency, we have: c = 540 302400 = 560
Final Answer Therefore, the missing values are a = 670 , b = 301600 , and c = 560 .
Examples
Understanding inverse variation is crucial in many real-world applications. For instance, in photography, the intensity of light and the exposure time are inversely related. If you increase the intensity of light, you need to decrease the exposure time to get a properly exposed photo. Similarly, in economics, the price of a product and the quantity demanded are often inversely related; as the price increases, the quantity demanded decreases, assuming all other factors remain constant. These concepts help us make informed decisions and predictions in various fields.
The missing values in the table are calculated as follows: a = 670, b = 301600, and c = 560. These calculations are based on the inverse variation relationship between wavelength and frequency. Each value corresponds to specific wavelengths and frequencies of visible light colors.
;
