Q1.
Table 10.1 shows the speed of sound in a few media at atmospheric pressure. [Table 10.1: Speed of sound in different media at 15 °C — Solid / Steel / 5000 m s–1; Liquid / Water / 1500 m s–1; Gas / Air / 340 m s–1] 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.
Answer
(i) about 4.4 : 1 (ii) about 3.3 : 1
(i) ratio = vwater / vair
= 1500 m s⁻¹ ÷ 340 m s⁻¹
= 4.41 ≈ 4.4 → vwater : vair ≈ 4.4 : 1
(ii) ratio = vsteel / vwater
= 5000 m s⁻¹ ÷ 1500 m s⁻¹
= 3.33 ≈ 3.3 → vsteel : vwater ≈ 3.3 : 1
= 1500 m s⁻¹ ÷ 340 m s⁻¹
= 4.41 ≈ 4.4 → vwater : vair ≈ 4.4 : 1
(ii) ratio = vsteel / vwater
= 5000 m s⁻¹ ÷ 1500 m s⁻¹
= 3.33 ≈ 3.3 → vsteel : vwater ≈ 3.3 : 1
Notice that the ratios have no unit — m s⁻¹ divided by m s⁻¹ cancels. And combining the two, vsteel : vair = 5000 : 340 ≈ 14.7 : 1, which agrees with the chapter's statement that sound travels typically 15 – 20 times faster in solids than in air.
Why solid > liquid > gas: a sound wave moves by particles bumping into their neighbours. In steel the atoms are locked in place by strong bonds and are very close together, so a push is passed on almost instantly. In water the molecules are close but free to slide, so the push is passed on more slowly. In air the molecules are far apart and weakly interacting, so each one must travel a comparatively long way before it collides — the disturbance creeps along. Closer packing and stiffer bonding therefore mean a higher speed of sound.
Tip: the table is quoted at 15 ºC for a reason. Speed in a gas depends noticeably on temperature — air carries sound at 331 m s⁻¹ at 0 ºC but 344 m s⁻¹ at 22 ºC — so a speed for a gas is meaningless without a temperature.