Question

1 wavelength and frequency have a(n) quadratic relationship. as frequency increases, wavelength increases. this relationship is shown in the graph. for example, when the wavelength is 450nm, the frequency is 667 hz. when the wavelength decreases to 420nm, the frequency decreases to 715 hz. wavelength is the speed between two consecutive points on a wave, such as from one crest to another crest. as the wavelength decreases, waves get closer together, therefore decreasing the frequency, or how often a new wave appears.

Explanation:

The relationship between wavelength and frequency in waves (such as electromagnetic waves) is an inverse relationship. The formula \(c = \lambda f\) (where \(c\) is the speed of the wave, \(\lambda\) is the wavelength, and \(f\) is the frequency) shows that when frequency increases, wavelength decreases (since \(c\) is constant for a given medium). Wavelength is the distance between two consecutive points (like crests). When wavelength decreases, waves are closer together, which means the frequency (number of waves passing a point per unit time) increases.

Answer:

Wavelength and frequency have a(n) inverse relationship. As frequency increases, wavelength decreases. For example, when the wavelength is \(450nm\), if we assume \(c = 3\times10^{8}m/s\) (speed of light in vacuum), \(f=\frac{c}{\lambda}=\frac{3\times 10^{8}}{450\times10^{- 9}}\approx6.67\times10^{14}Hz\) (not \(667Hz\) as wrongly written in the original, likely a unit error). When the wavelength decreases to \(420nm\), \(f=\frac{3\times 10^{8}}{420\times10^{-9}}\approx7.14\times10^{14}Hz\) (not \(715Hz\) as wrongly written in the original, likely a unit error). Wavelength is the distance between two consecutive points on a wave. As the wavelength decreases, waves get closer together, therefore increasing the frequency.