Question

wavelength varies inversely with frequency. let \\(k\\) be the product of wavelength and frequency. complete the table using the inverse variation relationship.

\\(\

$$\begin{array}{|c|c|c|c|}\\hline \\text{visible light} & \\text{wavelength (m)} & \\text{frequency (thz)} & k \\\\ \\hline \\text{blue} & 450 & a & 301,500 \\\\ \\hline \\text{green} & 520 & 580 & b \\\\ \\hline \\text{yellow} & c & 540 & 302,400 \\\\ \\hline \\text{red} & 635 & 480 & 304,800 \\\\ \\hline \\end{array}$$

\\)

\\(a = \\) \\(b = 301,\\) \\(c = \\)

Explanation:

Identify the inverse variation relationship

The problem states that wavelength varies inversely with frequency, and \(k\) is defined as the product of wavelength and frequency:

$$k = \text{Wavelength} \times \text{Frequency}$$

Calculate the value of a

For Blue light:

• \(\text{Wavelength} = 450\)
• \(\text{Frequency} = a\)
• \(k = 301,500\)

Using the relationship:

$$450 \times a = 301,500$$

$$a = \frac{301,500}{450} = 670$$

Calculate the value of b

For Green light:

• \(\text{Wavelength} = 520\)
• \(\text{Frequency} = 580\)
• \(k = b\)

Using the relationship:

$$b = 520 \times 580 = 301,600$$

The input field for \(b\) is partially filled as \(b = 301,\Box\), so the missing part to fill in is \(600\).

Calculate the value of c

For Yellow light:

• \(\text{Wavelength} = c\)
• \(\text{Frequency} = 540\)
• \(k = 302,400\)

Using the relationship:

$$c \times 540 = 302,400$$

$$c = \frac{302,400}{540} = 560$$

Answer:

\(a =\) <blank>670</blank>
\(b = 301,\) <blank>600</blank>
\(c =\) <blank>560</blank>