Question

Suppose that water waves coming into a dock have a velocity of 1,2 m/s and a wavelength of 2.4m. With what frequency do these waves meet the dock?

Answer 1

`f = 0.5 Hz`

Explanation:

There is a formula for this

`v = lambda*f`

I always have to think about the formula. I don't remember it like I do `F = m*a`. But it is easy to put together thinking about the units that the 3 variables need to have.

Velocity would be in `m/s`.
Wave length would be in `m`.
Frequency would be in `Hz` (which is equivalent to `s^-1`).

So I juggle `v, lambda, and f` and put together the formula so that the units come out right.

Plugging the data into the formula and solving for `f`

1.2 m/s = 2.4 m*f#

`f = (1.2 cancel(m)/s)/(2.4 cancel(m)) = 0.5 s^-1 = 0.5 Hz`

Another way to do it:
Since the speed is 1.2 m/s and a wave is 2.4 m from peak to peak, it must have taken 2 seconds to go that 2.4 m. So the period is 2 seconds.

The relationship between frequency and period has another formula.

`"Frequency" = 1/"period" = 1/(2 s) = 0.5 s^-1`

Note: period is `T`. You may have seen `f = 1/T`.

I hope this helps,
Steve