Water waves have a wavelength of 3.6cm and speed of 18cms ^ -1 in deep water. If the waves enter shallow water…

Analyze the question: A wave moves from deep water into shallow water. We are given the wavelength and speed in deep water, and the wavelength in shallow water. We need the speed in shallow water.

Concept: When a wave changes medium (or depth), its frequency stays the same, because the frequency is set by the source. Speed and wavelength change together, linked by:

v = fλ, so v₁/λ₁ = v₂/λ₂

Solution:

Deep water:

• λ₁ = 3.6 cm
• v₁ = 18 cm/s

Frequency: f = v₁/λ₁ = 18 / 3.6 = 5 Hz

Shallow water:

• λ₂ = 2.0 cm
• f = 5 Hz (unchanged)

v₂ = fλ₂ = 5 × 2.0 = 10.0 cm/s

Check using the ratio: v₂ = v₁ × (λ₂/λ₁) = 18 × (2.0/3.6) = 10 cm/s ✓

Answer: C. 10.0 cm/s

Tip: When a wave crosses a boundary, remember that f stays constant, while v and λ change in the same proportion. Waves slow down in shallow water, so the wavelength gets shorter. Your answer should be less than 18 cm/s, which rules out any option above 18. Option D (10.8) comes from wrongly multiplying 18 by 0.6, so watch your ratios carefully.