Question

How many times more wavelengths occur in air than in water for an air temperature of 10°C if the speed of sound in water is 5220 km/h and the frequency of sound is 500 Hz?

Answer 1

Lets calculate the wavelength of the sound in water. But before we do that, we must transform the unit of the speed to m/s. We get:

5220 / 3,6 = 1450 m/s

So

$\begin{gathered} v=\lambda f \\ 1450=\lambda\times500 \\ \lambda=\frac{1450}{500} \\ \lambda=2.9\text{ m} \end{gathered}$

The wave of sound does not change the frequency as it goes through different mediums. So f = 500 Hz. The speed of sound in air is 340 m/s. Then we can say that:

$\begin{gathered} v=\lambda f \\ 340=\lambda\times500 \\ \lambda=\frac{340}{500} \\ \lambda=0.68\text{ m} \end{gathered}$

We can see how many times more wavelengths occur in air by calculating the ratio:

$\begin{gathered} R=\frac{2.9}{0.68} \\ R\cong4 \end{gathered}$

So wavelengths in air occur approximately 4 times more than in water.