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?

Answer 1

When a sound wave travels from air to water, the wave speed and wavelength both increase while the frequency remains constant due to the source's vibration frequency. The formula Uw = fλ illustrates that if one variable changes and frequency remains the same, then wavelength must adjust accordingly.

Step-by-step explanation:

When a sound wave transitions from one medium to another, like from air to water, its speed changes due to the differing densities and elastic properties of the mediums. According to the principle that the frequency (f) of the wave remains constant when it changes medium, as it is dependent on the source, the change in wave speed (Uw) results in a corresponding change in wavelength (λ).

The formula for wave speed is Uw = fλ, where Uw is the wave speed, f is the frequency, and λ is the wavelength. In air, the waves travel at 400 m/s and have a wavelength of 2 m, while underwater, they travel at 1,600 m/s with a wavelength of 8 m. Since the speed of the wave is proportional to the wavelength when the frequency is constant, it can be deduced that the frequency has not changed as the wave moved from air to water. This is because the increased speed in water is counterbalanced by an increase in wavelength, keeping the frequency the same.

Answer 2

The frequency of the wave has not changed.

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

`f=(v)/(\lambda)`

where v is the wave's speed and
`\lambda` is the wavelength.

Applying the formula:

- In air, the frequency of the wave is:

`f=(400 m/s)/(2 m)=200 Hz`

- underwater, the frequency of the wave is:

`f=(1600 m/s)/(8 m)=200 Hz`

So, the frequency has not changed.