Question

As ocean waves approach the shore, friction with the ocean bottom causes them to slow down. If the frequency is the same, how will this affect the wavelength of the waves?

Answer 1

I would say it decreases as well.

Explanation:

The wave velocity will depends upon frequency and wavelength.
If the velocity decreases to maintain the same frequency the wavelength should also decrease.

For example:
let's say that we have a velocity of `100m/s` and frequency `10Hz` (I invented "easy" numbers for clarity).
We can say that:
`"velocity"="wavelength"xx"frequency"`
in our case:
`100=lambdaxx10`
or a wavelength: `lambda=100/10=10m`

Now, imagine a decrease to a velocity of, say, `50m/s`. But the frequency must remain `10Hz`.
Using again our expression:
`50=lambda_1xx10`
and the new wavelength: `lambda_1=50/10=5m`