Answer:
The frequency of this wave is [tex]3\; \rm Hz[/tex].
Explanation:
The frequency [tex]f[/tex] 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 [tex]v = 15\; \rm m \cdot s^{-1}[/tex]. In other words, this wave covers [tex]15\; \rm m[/tex] in unit time (a second.) How many wavelengths [tex]\lambda[/tex] would that [tex]15\; \rm m\;[/tex] correspond to?
The question states that the wavelength of this wave is [tex]\lambda = 5\; \rm m[/tex]. Therefore, there would be [tex]15 / 5 = 3[/tex] wavelengths in the [tex]15\; \rm m[/tex] span that this wave covered in the unit time of one second ([tex]1\; \rm s[/tex].) Hence, the frequency of this wave would be [tex]3\; \rm s^{-1}[/tex] (three per second,) which is equivalent to [tex]3\; \rm Hz[/tex] (three Hertzs.)
In general, the frequency [tex]f[/tex] of a wave with speed [tex]v[/tex] and wavelength [tex]\lambda[/tex] would be:
[tex]\displaystyle f = \frac{v}{\lambda}[/tex].
For the wave in this question:
[tex]\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}[/tex].
