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The equation of a wave is represented by: y = 10 sin [100t − x]. The velocity of the wave will be:

1. 100 m/s
2. 250 m/s
3. 750 m/s
4. 1000 m/s

Correct answer: 100 m/s

Solution

The wave equation is of the form y = A sin(ωt − kx), where ω is the angular frequency and k is the wave number. The velocity of the wave is given by v = ω/k. Here, ω = 100 rad/s and k = 1 m⁻¹ (from the coefficient of x). Thus, v = 100/1 = 100 m/s.

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