Question

Consider two waves moving past you at the same speed. The wavelength of wave A is half that of wave B. You then know that ____.

Answer 1

The frequency of wave B is half the frequency of wave A

Explanation:

The wavelength, the speed and the frequency of  a wave are related by the wave equation:

$v=f \lambda$

where

v is the speed of the wave

f is its frequency

$\lambda$ is its wavelength

The equation can also be rewritten as

$f=\frac{v}{\lambda}$

In this problem, we have wave A with wavelength $\lambda_A$ and speed v, so its frequency is

$f_A=\frac{v}{\lambda_A}$

Then we have wave B, whose wavelength is twice that of wave A:

$\lambda_B = 2 \lambda_A$

And its speed is the same; Therefore, its frequency is

$f_B = \frac{v}{\lambda_B}=\frac{v}{2\lambda_A}=\frac{1}{2}(\frac{v}{\lambda_A})=\frac{f_A}{2}$

So, the frequency of wave B is half that of wave A.

Learn more about wavelength and frequency:

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