The time elapsed between viewing a lightning flash and hearing the thunder of a cloud is 10 s. If the speeds of sound and light in air are 330 m/s and 3 × 10^8 m/s respectively, how far away is the storm?

Correct — B, About 3300 m. The gap between the flash and the bang is almost entirely the time sound needs to cover the distance. Light crosses a few kilometres in roughly a hundred-thousandth of a second, so the eye sees the flash effectively at the instant it happens. That leaves the whole 10 s to the sound wave: 330 m/s × 10 s = 3300 m. Put the light leg in and nothing changes — 3300 ÷ (3 × 10⁸) is about 1.1 × 10⁻⁵ s, which would shave a hundredth of a millimetre off the answer.

• (a)About 1650 m — 1650 m is what a 5-second gap would give. Halving the correct distance suggests the 10 s was split between the two journeys, but light contributes no measurable share of it.
• (c)About 990 m — 990 m is 330 × 3. A 3-second count is the rule of thumb for one kilometre, and picking this option means answering the familiar version of the question rather than the printed one.
• (d)About 1000 m — 1000 m is a round number with no arithmetic behind it. Sound would need 3.03 s to cover it, not the 10 s the stem gives.

Light and sound leave a lightning channel at the same moment but arrive far apart, because sound in air moves at a few hundred metres a second while light moves at 3 × 10⁸ m/s — a ratio close to a million to one. Over any distance a person can hear thunder from, the light leg is unmeasurable, so the counted interval is the sound's travel time alone and distance = 330 × t.

The examiner supplies the speed of light only to see whether you will use it. A candidate who tries to be thorough sets up distance/330 − distance/(3 × 10⁸) = 10 and loses a minute solving it, and the second term is smaller than the first by a factor of about a million. Field practice compresses this further: dividing the count by three gives kilometres (330 × 3 ≈ 1 km), so 10 s is a little over 3 km. That estimate alone separates 3300 m from every other option on the page.

• Sound in dry air near room temperature travels at roughly 330-343 m/s; light travels at 3 × 10⁸ m/s.
• Distance to a storm ≈ 330 × (seconds counted between flash and thunder).
• Dividing the count in seconds by 3 gives the distance in kilometres, and by 5 gives it in miles.
• The light delay over 3300 m is about 1.1 × 10⁻⁵ s, which no hand-timed count can register.
• Sound speeds up as air warms — about 0.6 m/s for every degree Celsius — so 330 m/s is a cool-air value.

• Splitting the 10 s between light and sound, which halves the distance to 1650 m.
• Using the 3-second-per-kilometre rule of thumb but reading it as a 3-second total.
• Converting units carelessly — 330 m/s is metres, so the answer comes out in metres, not kilometres.

Set as a one-step speed-distance-time sum wrapped in a physics story; the speed of light is a decoy the examiner plants to test judgement about which quantity actually matters.

• practice — not a real PYQ

  A person hears the thunder 6 s after seeing the lightning. Taking the speed of sound as 340 m/s, how far away is the discharge?

  • (a)1020 m
  • (b)1700 m
  • (c)2040 m
  • (d)2400 m

  Answer(c) 2040 m — 340 × 6 = 2040 m; the light travel time is negligible.

• practice — not a real PYQ

  An echo is heard 0.8 s after a shout, with the speed of sound at 340 m/s. How far away is the reflecting wall?

  • (a)68 m
  • (b)136 m
  • (c)272 m
  • (d)340 m

  Answer(b) 136 m — the sound covers the distance twice, so 340 × 0.8 = 272 m of path, and the wall is at half that.