NDA (II) 2022 General Ability Test · Question 146 of 150

Correct — B, the claim that the speed of sound waves in air decreases with increase in temperature. The question asks which statement is not correct, so the answer is the false one, and this is it. Sound in a gas travels faster when the gas is hotter, because the speed depends on the square root of the absolute temperature — the molecules move faster and pass the disturbance along more quickly. In dry air the speed is about 331 metres per second at zero degrees Celsius and rises by roughly 0·6 metres per second for every degree of warming. Options (b) and (c) directly contradict each other, so one of them has to be the false statement, and (c) is the true one — which settles the matter without needing to check the other two.

• (a)The speed of sound waves in steel is higher than that in water. — This is true, so it cannot be the answer to a which-is-not-correct question. Sound travels fastest in solids because they are far more rigid than liquids, and steel carries sound at several thousand metres per second against roughly 1500 in water.
• (c)The speed of sound waves in air increases with increase in temperature. — This is the correct statement of the temperature effect, and it is the exact opposite of option (b). Being true, it is not the answer to this negative-form question.
• (d)The speed of sound waves in water is higher than that in air. — Also true. Sound is a mechanical wave carried by the elastic properties of the medium, and water is far less compressible than air, so sound moves through it about four times as fast.

Sound is a longitudinal mechanical wave, so it needs a material medium and cannot travel through a vacuum. Its speed is set by the medium, not by the source — by the balance between the elasticity of the medium and its density. Solids are the most elastic and carry sound fastest, liquids come next and gases are slowest, which is the reverse of the intuitive expectation that a light medium should be quick. Within a gas the speed rises with absolute temperature as its square root, and it is essentially independent of pressure, since a change of pressure alters density and elasticity together. Humidity raises the speed slightly, because water vapour is lighter than the air it displaces.

Negative-form questions are where careless reading costs marks, and this one gives an unusually generous shortcut. Two of the four options are exact contradictions of each other, so the false statement must be one of that pair; the rest of the option set is decoration. Beyond the trick, the ordering to fix is the solid-liquid-gas sequence for speed, and the temperature rule for air. The point that catches many students is the mistaken analogy with the falling density of hot air — a hotter gas is less dense, which would slow a wave if density alone mattered, but the elasticity term rises faster, so the net effect is an increase. Frequency, incidentally, has no effect on the speed of sound in a given medium; changing the frequency changes the wavelength instead.

• Sound is a longitudinal mechanical wave and cannot travel through a vacuum.
• The speed of sound is highest in solids, lower in liquids and lowest in gases.
• In dry air, sound travels at about 331 m s⁻¹ at 0 °C and the speed rises by roughly 0·6 m s⁻¹ per degree Celsius.
• The speed of sound in a gas varies as the square root of the absolute temperature and is essentially independent of pressure.
• In a given medium the speed of sound does not depend on the frequency; changing frequency changes wavelength instead.

• Reading past the word not in the stem and marking a true statement.
• Reasoning that hot air is less dense and therefore slower, when the elasticity term dominates.
• Believing that a higher-pitched note travels faster than a lower one in the same medium.

As a which-statement-is-not-correct item, or as a comparison of the speed of sound across different media.

• practice — not a real PYQ

  In which one of the following media does sound travel fastest?

  • (a)Vacuum
  • (b)Air at 0 °C
  • (c)Water
  • (d)Iron

  Answer(d) Iron — sound travels fastest in solids because of their high elasticity, and not at all in a vacuum.

• practice — not a real PYQ

  If the temperature of air rises, the speed of sound in it

  • (a)increases
  • (b)decreases
  • (c)remains unchanged
  • (d)first decreases and then increases

  Answer(a) increases — the speed varies as the square root of the absolute temperature, rising by about 0·6 m s⁻¹ per degree Celsius near room temperature.