Question

consider two waves of light, a and b. wave a has a higher frequency than wave b. therefore, wave b must have a higher speed. lower speed. shorter wavelength. this cant be determined from the information given. longer wavelength.

Explanation:

The speed of light waves in a vacuum is constant (\(c = 3\times10^{8}\ m/s\)). The relationship between speed (\(c\)), frequency (\(f\)), and wavelength (\(\lambda\)) is \(c=\lambda f\). Rearranging for \(\lambda\) gives \(\lambda=\frac{c}{f}\). Since \(c\) is constant, if wave \(A\) has a higher frequency (\(f_A>f_B\)), then \(\lambda_B=\frac{c}{f_B}\) and \(\lambda_A = \frac{c}{f_A}\). Because \(f_A>f_B\), \(\frac{c}{f_A}<\frac{c}{f_B}\), so \(\lambda_A<\lambda_B\).

Answer:

longer wavelength.