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A standing wave is represented by y = A sin (100t) cos (0.01x), where y and A are in millimetre, t in seconds and x in metre. Velocity of wave is

1. 10⁴ m/s
2. 1 m/s
3. 10⁻⁴ m/s
4. not derivable from above data

Correct answer: 10⁴ m/s

Solution

The given equation y = A sin(100t) cos(0.01x) represents a standing wave. The angular frequency ω = 100 rad/s and the wave number k = 0.01 rad/m. The wave velocity is given by v = ω/k = 100/0.01 = 10⁴ m/s.

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