Consider the following statements with reference to Secondary waves (S-Waves) generated during an earthquake: 1. They create troughs and crests in the material through which they pass. 2. The direction of vibrations of S-waves is perpendicular to the wave direction in the vertical plane. Which of the statements given above is/are correct?

Correct — C, Both 1 and 2. Secondary waves are transverse body waves: the particles of the rock they pass through move at right angles to the direction the wave is travelling. Statement 2 says exactly that, adding that for an S-wave the shaking is taken in the vertical plane. Statement 1 is the visible consequence of the same physics — if every particle is displaced sideways to the line of travel, the disturbed material is thrown into a train of crests and troughs, the shape of a rope flicked at one end. Compare the primary wave, which vibrates along the line of travel and therefore squeezes and stretches the rock into alternate zones of higher and lower density instead of humps and hollows. Because both statements describe the same single property of S-waves from two sides, there is no reading on which one is true and the other false, and the answer is both.

• (a)1 only — Accepts the crests and troughs but rejects the perpendicular vibration that produces them. The two cannot be separated — a wave that made crests and troughs while vibrating along its own direction of travel would be a contradiction.
• (b)2 only — Accepts the perpendicular vibration but denies its consequence. Sideways particle motion is precisely what leaves a wave-form of humps and hollows in the material.
• (d)Neither 1 nor 2 — Both statements are correct. This option would fit the primary wave, which vibrates parallel to the direction of travel and creates density differences rather than crests and troughs.

An earthquake sends out body waves, which travel through the interior of the Earth, and surface waves, which travel along the crust. The two body waves are the primary (P) wave, a longitudinal wave whose particles vibrate along the direction of travel, and the secondary (S) wave, a transverse wave whose particles vibrate at right angles to it. P-waves are faster and arrive first; S-waves lag behind, and the gap between the two arrivals on a seismograph is what lets seismologists work out how far away the epicentre lies.

The trap here is the phrase 'troughs and crests', which most students file under water waves or surface waves and therefore hesitate to attach to a body wave. Reason it out physically instead of by association: any transverse disturbance, in a rope, on a pond or in rock, shows up as crests and troughs, because that is what displacement perpendicular to the line of travel looks like. The second statement hands you the perpendicular vibration, so the first follows from it. A second, more useful property of S-waves is not tested here but is worth carrying away — they pass only through solids, which is how we know the outer core is liquid.

• P-waves vibrate parallel to the direction of travel and so exert pressure along it, creating density differences — stretching and squeezing — in the material.
• S-waves vibrate perpendicular to the direction of travel in the vertical plane and so create troughs and crests in the material they pass through.
• P-waves travel through gaseous, liquid and solid material; S-waves travel only through solids, which is the evidence that the outer core is liquid.
• Seismographs within 105 degrees of the epicentre record both P and S-waves; the belt between 105 and 145 degrees is the shadow zone for both, and no station beyond 105 degrees receives S-waves at all.
• Surface waves are the last to be recorded on a seismograph and are the most destructive.

• Reading 'crests and troughs' as a property only of surface or water waves and rejecting it for S-waves.
• Swapping the two body waves — it is the P-wave that creates density differences by squeezing and stretching.
• Assuming the S-wave shadow zone is the same band as the P-wave shadow zone; the entire region beyond 105 degrees from the epicentre receives no S-waves.

Usually as a two-statement item on the vibration direction, speed, or medium a named wave can pass through, or as a 'which statement is not correct' item that hides one swapped property.

• practice — not a real PYQ

  The fact that S-waves are not recorded beyond a certain distance from the epicentre is the main evidence for which one of the following?

  • (a)The crust is thinner under the oceans than under the continents
  • (b)The outer core of the Earth is in a liquid state
  • (c)The inner core of the Earth is solid
  • (d)The mantle is made of silicate rock

  Answer(b) The outer core of the Earth is in a liquid state — S-waves travel only through solids, so their failure to cross the outer core shows that layer is not solid.

• practice — not a real PYQ

  Which one among the following statements about primary waves generated during an earthquake is correct?

  • (a)They vibrate perpendicular to the direction of travel
  • (b)They are the last to be recorded on a seismograph
  • (c)They create density differences in the material through which they pass
  • (d)They cannot pass through liquids

  Answer(c) They create density differences in the material through which they pass — the P-wave vibrates along its direction of travel, so it squeezes and stretches the rock.