Question

A wave has a frequency of 40 hertz and a wavelength of 2 meters . what is the wave speed ?

Answer 1

`80\; {\rm m\cdot s^(-1)}`.

Step-by-step explanation:

The frequency
`f` of a wave is the number of cycles completed in unit time (
`1\; {\rm s}` in this example.) In this question,
`f = 40\; {\rm s^(-1)}` (
`1\; {\rm Hz} = 1\; {\rm s^(-1)}`) means that the wave would complete
`40` cycles in every
`1\; {\rm s}`.

The wavelength
`\lambda` of a wave is the distance the wave travels in each cycle. It is given that
`\lambda = 2\; {\rm m}`.

The goal is to find the wave speed, which is the distance that this wave travels in unit time (
`1\; {\rm s}`.)

In this question, it is given that
`\lambda = 2\; {\rm m}` and
`f = 40\; {\rm s^(-1)}`. Thus, this wave would travel a total of
`40\, (2\; {\rm m}) = 80\; {\rm m}` for the
`40` cycles completed in each unit time of
`1\; {\rm s}` (
`\lambda = 2\; {\rm m}` for each cycle.) The speed of this wave would be
`80\; {\rm m\cdot s^(-1)}`.

Formally, the speed
`v` of this wave can be found by multiplying the wavelength
`\lambda` of this wave by its frequency
`f`:

`\begin{aligned}v &= \lambda\, f \\ &= (2\; {\rm m})\, (40\; {\rm s^(-1)) \\ &= 80\; {\rm m\cdot s^(-1)}\end{aligned}`.