Question

Dolphins make sounds in air and water. What is the ratio of the wavelength of a sound in air to its wavelength in seawater? Assume air temperature is $\mathbf{20}\mathbf{.}{\mathbf{0}}^{\mathbf{\circ }}\mathit{C}$.

Short answer

The ratio is 0.22

Step-by-step solution

Given Data

The temperature is$T=0.{20}^{\circ }C$.

The sound waves’ speed is $V_{seawater}=1540m/s$.

Explanation

A proportional increase, with an increase in temperature, is observed in the velocity of a sound wave traveling in a gaseous medium.

Calculation of the speed

The speed of a wave is given by,

$v=331+0.6T$

Plugging the values,

$$\begin{gathered} v=331+0.6\times 20.0^{\circ }C \\ =343m/s \end{gathered}$$

The ratio of the speeds is,

$$\begin{gathered} \frac{v}{V_{seawater}}=\frac{343m/s}{1540m/s} \\ =0.22 \end{gathered}$$

The ratio between the two velocities is 0.22 .