CDS (II) 2023 General Knowledge · Question 35 of 120

Correct — B, Stainless steel. Sound is a mechanical wave, so it travels by making the particles of a medium push on their neighbours. Its speed is set by two competing properties: it rises with the stiffness of the medium and falls with the medium's density. Going from a gas to a liquid to a solid, density rises a great deal but stiffness rises far more, which is why sound is slowest in gases, faster in liquids and fastest in solids. That ordering settles two of the four options at once. Oxygen is a gas and carries sound at only a few hundred metres per second — of the order of 320 to 330 m/s, close to air's 343 m/s at 20 degrees Celsius. Water is a liquid at 1,481 m/s at 20 degrees Celsius, roughly four and a half times faster than the gas but still far behind any metal. That leaves two solids, and among them stainless steel is the faster: the longitudinal speed in stainless steel 304 is about 5,912 m/s. Glass is genuinely fast as well, but published values for it span a wide band from roughly 4,000 m/s for flint glass to about 5,600 m/s for a borosilicate glass, and even the top of that band sits below stainless steel. So steel wins on the numbers as well as on the intuition that a metal rings.

• (a)Glass — The only serious rival, because glass is a stiff solid and does carry sound at several thousand metres per second. But glass is not one material with one number — reported speeds run from about 4,000 m/s for flint glass to about 5,600 m/s for borosilicate — and the whole range lies under stainless steel's figure of roughly 5,900 m/s.
• (c)Water — Water is a liquid: about 1,481 m/s at 20 degrees Celsius. It beats every gas comfortably but is roughly four times slower than steel, because a liquid resists being squeezed far less stiffly than a metal does.
• (d)Oxygen — A gas, and therefore the slowest of the four by a wide margin — of the order of 320 m/s, in the same range as ordinary air. Gas molecules are far apart, so a disturbance is passed on slowly.

The speed of a sound wave in a medium is given by the square root of an elastic modulus divided by the density — the Newton-Laplace relation. Stiffness is what carries the disturbance forward; inertia is what holds it back. From air to steel the density rises by a factor of several thousand, but the stiffness rises by a factor of roughly a million, so the ratio comes out overwhelmingly in the solid's favour. This is the reasoning behind the familiar ordering: solids fastest, liquids next, gases slowest.

The safe route is to sort by state of matter first, which immediately eliminates oxygen and water, and then to decide between the two solids. That second step is the real content of the question and it is worth being careful about, because a candidate who reasons only from 'solids are fast' cannot separate glass from steel. The honest statement is that stainless steel at about 5,900 m/s sits above the common glasses, whose published speeds vary with composition. In a gas the speed depends on temperature and on molar mass rather than on pressure, which is why sound is faster in warm air than in cold and faster in hydrogen than in any other gas. These are settled physical constants, so nothing about the answer has moved since the 2023 exam.

• Longitudinal speed of sound in stainless steel 304 is about 5,912 m/s.
• In water at 20 degrees Celsius the speed is 1,481 m/s; in air at the same temperature it is 343.2 m/s, and oxygen is in the same range as air.
• Sound 'travels most slowly in gases, faster in liquids, and fastest in solids' — the speed 'increases with the stiffness of the material and decreases with an increase in density'.
• Glass has no single speed: reported values range from about 4,000 m/s for flint glass to about 5,600 m/s for borosilicate, all below stainless steel.
• In a gas the speed rises with temperature and falls with molar mass, which is why hydrogen is the fastest common gas.

• Assuming sound travels fastest in the densest material. Density slows sound down; it is stiffness that speeds it up, and steel wins despite being far denser than air.
• Treating glass as having a single textbook speed. It varies with composition, which is exactly why the safe comparison is with the top of its range.
• Carrying over the light-wave intuition that a wave slows in a denser medium — for sound the ordering is the other way round.

As a four-medium ranking item, or as a statements question mixing the state-of-matter ordering with the temperature dependence in gases.

• practice — not a real PYQ

  The speed of sound in a medium increases with which one of the following?

  • (a)An increase in the density of the medium
  • (b)An increase in the stiffness of the medium
  • (c)An increase in the frequency of the sound
  • (d)An increase in the pressure of a gas at constant temperature

  Answer(b) An increase in the stiffness of the medium — speed goes as the square root of the elastic modulus divided by density, so stiffness raises it while density lowers it; frequency and gas pressure at constant temperature do not change it.

• practice — not a real PYQ

  Which one of the following lists the media in the correct order of increasing speed of sound?

  • (a)Steel, water, air
  • (b)Water, air, steel
  • (c)Air, water, steel
  • (d)Air, steel, water

  Answer(c) Air, water, steel — sound is slowest in gases, faster in liquids and fastest in solids, so about 343 m/s in air, 1,481 m/s in water and some 5,900 m/s in steel.