Question

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?
it increased.
it decreased.
it stayed the same.
it cannot be calculated.

Explanation:

Step1: Recall the wave - speed formula

The formula for the speed of a wave is \(v = f\lambda\), where \(v\) is the speed of the wave, \(f\) is the frequency, and \(\lambda\) is the wavelength.

Step2: Calculate the frequency in air

In air, \(v = 400\space m/s\) and \(\lambda=2\space m\). Using \(v = f\lambda\), we can solve for \(f\): \(f=\frac{v}{\lambda}\). So, \(f_{air}=\frac{400}{2}=200\space Hz\).

Step3: Calculate the frequency underwater

Underwater, \(v = 1600\space m/s\) and \(\lambda = 8\space m\). Using \(v = f\lambda\), we solve for \(f\): \(f=\frac{v}{\lambda}\). So, \(f_{water}=\frac{1600}{8}=200\space Hz\).

Answer:

It stayed the same.