a) What is the speed of sound in a medium where a 100 kHz frequency produces a 5.96 cm wavelength? (b) Which substance in Table 17.1 is this likely to be?

The frequency is \(f = 100\;{\rm{kHz}} = 100 \times {10^3}\;{\rm{Hz}}\).

The wavelength is \(\lambda = 5.96\;{\rm{cm}} = 5.96 \times {10^{ - 2}}\;{\rm{m}}\).

If we compare the speeds of sound in the three states of matter, we will see that the sound travels the fastest in solids, comparatively slower in liquids, and the slowest in gasses. This is the reason the sound of the train can be heard by putting the ear on the rails, long before the sound reaches us through the air.

The speed of a wave is given by,

$\mathit{v}\mathbf{=}\mathit{f}\mathit{\lambda }$

For, $\lambda =5.96\times {10}^{-2}m$and $f=100\times {10}^{3}Hz$,

$$\begin{gathered} v=\left(100\times {10}^3\right)Hz\times 0.05960m \\ =5960m/s \end{gathered}$$

(b) Speed of sound in steel is 5960 m/s .

The speed of sound we have calculated is 5960 m/s ,

According to the calculated velocity the material is steel.