40% off

Ends in

--d--h--mLock in £90
← All past papers

ESAT Mock Physics Esat-physics-tp6-1

3 questions3 marks40Updated August 2026

The ESAT Mock Physics Esat-physics-tp6-1 paper in full: all 3 questions, each with its answer. ESAT is the Engineering and Science Admissions Test. Sit it cold under exam timing, mark it, then work back through anything you missed using the solutions below.

Questions and answers are free. Full step-by-step worked solutions unlock with a free account. Start practising.

Question 1

1 mark
A boat is anchored at sea and bobs up and down as water waves pass beneath it, completing one full oscillation every 2.5 s2.5\,\text{s}. A wave crest passes the boat, and the next crest passes a fixed buoy 30 m30\,\text{m} further along the direction of wave travel exactly 12.0 s12.0\,\text{s} later. The buoy is known to be between 33 and 44 wavelengths from the boat.

What is the speed of the wave?
  • A.2.0 ms−12.0\,\text{ms}^{-1}
  • B.6.0 ms−16.0\,\text{ms}^{-1}
  • C.2.5 ms−12.5\,\text{ms}^{-1}
  • D.5.0 ms−15.0\,\text{ms}^{-1}
  • E.7.5 ms−17.5\,\text{ms}^{-1}
  • F.3.75 ms−13.75\,\text{ms}^{-1}
  • G.3.0 ms−13.0\,\text{ms}^{-1}

Answer: G

Full step-by-step worked solution

Locked. Available with a free account.

Unlock worked solutions →

Question 2

1 mark
A loudspeaker emits a sound wave of frequency ff and wavelength λ\lambda in air, where the speed of sound is vv. The sound wave enters a long tube filled with a different gas, in which the speed of sound is 32v\dfrac{3}{2}v.

A particle of air just outside the tube entrance and a particle of the second gas exactly one wavelength (measured in the second gas) into the tube both start from rest at their equilibrium positions at the same instant, moving in the same direction, as the wave enters the tube.

Which of the following statements about these two particles is correct once the wave has fully established itself in the tube?
  • A.The phase difference cannot be determined without knowing the wavelength in air.
  • B.The two particles differ in phase by two thirds of a period, with the particle in the gas leading.
  • C.The two particles differ in phase by one third of a period, with the particle in the gas leading.
  • D.The two particles differ in phase by one third of a period, with the particle in air leading.
  • E.The two particles are exactly out of phase, differing by half a period.
  • F.The two particles always move in phase, since frequency is unchanged across the boundary.

Answer: F

Full step-by-step worked solution

Locked. Available with a free account.

Unlock worked solutions →

Question 3

1 mark
A longitudinal wave travels along a spring at constant speed vv. At a particular instant, a compression (a region of maximum crowding of coils) is located at position CC, and the nearest rarefaction (a region of maximum spreading of coils) to the right of CC is located a distance dd away, as shown.

A fixed point PP on the spring lies exactly halfway between CC and the rarefaction at this instant, and PP is currently moving to the right (in the direction the coils would move for a compression to pass).

How long after this instant will the point PP next be at a compression?
  • A.8dv\dfrac{8d}{v}
  • B.dv\dfrac{d}{v}
  • C.6dv\dfrac{6d}{v}
  • D.2dv\dfrac{2d}{v}
  • E.4dv\dfrac{4d}{v}
  • F.3dv\dfrac{3d}{v}

Answer: F

Full step-by-step worked solution

Locked. Available with a free account.

Unlock worked solutions →
ESAT Mock Physics Esat-physics-tp6-1: Questions & Worked Solutions | esat.fyi