# A wave has a wavelength of 5 meters and a frequency of 3 hertz. What is the speed of the wave?

Oct 10, 2017

The speed of the wave is $15 \frac{m}{s}$.

#### Explanation:

There are 2 ways to help with this. Explain the details, which are fairly simple in this topic, or give the formula. My hope is that an explanation will last longer than memorizing the formula. I give you both.

If a wave has frequency, f, of 3 Hz, its period, T, is $\frac{1}{3} s$. The wavelength, $\lambda$, is 5 meters. That means that in the time of one period, the wave travels 5 m.

In general, $\text{ "Speed = "distance"/"time}$

In applying this general definition of speed$\uparrow$to a wave, we have
$\text{ speed of the wave" = "wavelength"/"period}$

Note: we generally use v for speed of a wave. Using the variable names, then that last formula is written
$v = \frac{\lambda}{T}$
Since $T = \frac{1}{f}$, we can also say that

$v = \lambda \cdot f$

So, using that last formula
$v = 5 m \cdot 3 H z = 15 \frac{m}{s}$

Note: the unit Hz is equivalent to what it was called 100 years ago, "cycles"/"second" ("also cps"). Cycles is not a true unit, so the Hz contributed only the "per second" to the result $15 \frac{m}{s}$.

I hope this helps,
Steve