Question

microwaves have low frequencies. what does that tell us about their wavelengths?
they have short wavelengths.
they have long wavelengths.
wavelength is unrelated to frequency.

Explanation:

Step1: Recall the relationship between frequency and wavelength

The formula for the speed of a wave is \(c = \lambda f\), where \(c\) is the speed of light (a constant in a vacuum, \(c\approx3\times 10^{8}\space m/s\)), \(\lambda\) is the wavelength, and \(f\) is the frequency. Rearranging for wavelength gives \(\lambda=\frac{c}{f}\).

Step2: Analyze the effect of low frequency on wavelength

Since \(c\) is constant, when \(f\) (frequency) is low, the value of \(\frac{c}{f}\) (wavelength) is large. For example, if \(f_1 < f_2\), then \(\lambda_1=\frac{c}{f_1}>\lambda_2 = \frac{c}{f_2}\)

Answer:

They have long wavelengths.