Exercise 10.10
Table shows the speed of sound in a few media at atmospheric pressure. Compare the speeds in different media by finding the ratio of (i) the speed of sound in water with respect to the speed in the air. (ii) the speed of sound in steel with respect to the speed in the water.
NCERT’s answer
(i)
$\displaystyle 75$:$\displaystyle 17$ (ii) $\displaystyle 10$:$\displaystyle 3$
(i) water : air = $\displaystyle 75$ : 17. (ii) steel : water = $\displaystyle 10$ : 3.
From Table $\displaystyle 10.1$ at $\displaystyle 15$ ºC: steel \(\displaystyle 5000\ \text{m s}^{-1} \), water \(\displaystyle 1500\ \text{m s}^{-1} \), air \(\displaystyle 340\ \text{m s}^{-1} \).
(i) \(\displaystyle \dfrac{v_{\text{water}}}{v_{\text{air}}} = \dfrac{1500}{340} = \dfrac{150}{34} = \dfrac{75}{17} \approx 4.4 \) — sound is about $\displaystyle 4$–$\displaystyle 5$ times faster in water than in air.
(ii) \(\displaystyle \dfrac{v_{\text{steel}}}{v_{\text{water}}} = \dfrac{5000}{1500} = \dfrac{10}{3} \approx 3.3 \) — and steel is about $\displaystyle 15$ times faster than air.
Both ratios confirm the chapter's ordering: sound is fastest in solids, slower in liquids and slowest in gases.