Voices of swimmers at a pool travel 400 m/s through the air and 1,600 m/s underwater. the wavelength changes from 2 m in the air to 8 m underwater. how has the change in media affected the frequency of the wave?

The frequency of the wave has not changed.

In fact, the frequency of a wave is given by:

where v is the wave's speed and is the wavelength.

Applying the formula:

- In air, the frequency of the wave is:

- underwater, the frequency of the wave is:

So, the frequency has not changed.

The change in media affected the frequency by a quarter.

The sound velocity (), in meters per second, is described by the following expression:

(1)

Where:

By (1), we get expression for the frequency:

Now we proceed to determine the frequency associated to each medium:

Water (, )

Air (, )

The change in media affected the frequency by a quarter.

We kindly invite to check this question on wavelengths: link