Question

analyze the relationship between wavelength and frequency in the electromagnetic spectrum. if wave x has twice the wavelength of wave y, how does the frequency of wave x compare to wave y? wave x has twice the frequency of wave y wave x has half the frequency of wave y wave x has the same frequency as wave y there is no consistent relationship between wavelength and frequency

Explanation:

In the electromagnetic spectrum, the speed of light \( c \) (a constant) is related to wavelength \( \lambda \) and frequency \( f \) by the formula \( c = \lambda f \). If Wave X has twice the wavelength of Wave Y (\( \lambda_X = 2\lambda_Y \)) and the speed \( c \) is constant, we can substitute into the formula. For Wave Y: \( c=\lambda_Y f_Y \), for Wave X: \( c = \lambda_X f_X=2\lambda_Y f_X \). Since \( c \) is the same, \( \lambda_Y f_Y=2\lambda_Y f_X \). Dividing both sides by \( \lambda_Y \) (assuming \( \lambda_Y
eq0 \)), we get \( f_Y = 2f_X \), so \( f_X=\frac{1}{2}f_Y \). This means Wave X has half the frequency of Wave Y.

Answer:

B. Wave X has half the frequency of Wave Y