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

Answer:

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

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:

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

For the wave in this question:

$\begin{aligned}f &= \frac{v}{\lambda} \\ &= \frac{15\; \rm m \cdot s^{-1}}{3\; \rm s} = 3\; \rm s^{-1} = 3\; \rm Hz\end{aligned}$.