ARCH-P-11: Wave Equation (v = fλ), Refraction Invariance, Pulse-Echo Sonar (d = ½vt), Relative Waves & Redshift

Full 15-Q Timed Drill

Step 1 of 6 • The Core Idea

ARCH-P-11: Why the 130s Classroom Method Fails Under the 90s Clock

Standard Classroom Method (Too Slow)~130s (Blows 90s Clock)

In one complete oscillation, a particle moves from

0 \to +3\text{ cm} \to 0 \to -3\text{ cm} \to 0

, covering

4 \times 3 = 12\text{ cm}

. In

1\text{ min} = 60\text{ s}

, the particle completes

N = f t = 4 \times 60 = 240

cycles, travelling

12 \times 240 = 2880\text{ cm}

(~115s).

The Fast ShortcutTarget: 35s (Saves 95s)

**Line 1 (Ignore

\lambda

, Use

4A

per Cycle):** Wavelength

\lambda = 5\text{ cm}

is a distractor! Distance per cycle

= 4A = 12\text{ cm}

.
**Line 2 (Multiply by

60 f t_{\text{min}}

):**

d = 12 \times 4 \times 60 = 2880\text{ cm}

(25s).

Where Students Lose Time: In 35 past UAT-UK questions (15.02% of Physics), candidates lose 95s by forgetting that pulse-echo time t is a round trip (2d) and one full transverse oscillation covers 4 amplitudes (4a). Instead, apply P6 with Maths 1 skill M1.2.

Step 1 of 6 • Press ArrowRight or Space