Question

A wave is traveling at a speed of 15 m/s and it's wavelength is 5 m. Calculate the waves frequency

Answer 1

The frequency of this wave is
`3\; \rm Hz`.

Step-by-step explanation:

The frequency
`f` of a wave is the number of wavelengths that this wave covers in unit time (typically a second.)

The wave in this question travels at
`v = 15\; \rm m \cdot s^(-1)`. In other words, this wave covers
`15\; \rm m` in unit time (a second.) How many wavelengths
`\lambda` would that
`15\; \rm m\;` correspond to?

The question states that the wavelength of this wave is
`\lambda = 5\; \rm m`. Therefore, there would be
`15 / 5 = 3` wavelengths in the
`15\; \rm m` span that this wave covered in the unit time of one second (
`1\; \rm s`.) Hence, the frequency of this wave would be
`3\; \rm s^(-1)` (three per second,) which is equivalent to
`3\; \rm Hz` (three Hertzs.)

In general, the frequency
`f` of a wave with speed
`v` and wavelength
`\lambda` would be:

`\displaystyle f = (v)/(\lambda)`.

For the wave in this question:

`\begin{aligned}f &= (v)/(\lambda) \\ &= (15\; \rm m \cdot s^(-1))/(3\; \rm s) = 3\; \rm s^(-1) = 3\; \rm Hz\end{aligned}`.