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The equation of a travelling wave is y = 60 cos (180 t − 6x) where y is in microns, t in second and x in metres. The ratio of maximum particle velocity to velocity of wave propagation is

1. 3.6
2. 3.6×10⁻⁶
3. 3.6×10⁻¹¹
4. 6×10⁻⁴

Correct answer: 3.6

Solution

The wave equation is y = 60 cos(180t − 6x). The maximum particle velocity is given by ωA, where ω = 180 rad/s and A = 60 × 10⁻⁶ m. Thus, maximum particle velocity = 180 × 60 × 10⁻⁶ = 10.8 × 10⁻³ m/s. The wave velocity is v = ω/k = 180/6 = 30 m/s. The ratio of maximum particle velocity to wave velocity is (10.8 × 10⁻³) / 30 = 3.6 × 10⁻⁴. Hence, the correct answer is A) 3.6.

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