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A particle in a medium has displacement given by y = 10⁻⁶ sin(100t + 20x + π/4) m, where t is measured in seconds and x in metres. What is the speed of the wave?

1. 20 m/s
2. 5 m/s
3. 2000 m/s
4. 5π m/s

Correct answer: 5 m/s

Solution

The speed of a wave can be determined from its wave equation, where the general form is y = A sin(ωt + kx). Here, ω (angular frequency) is 100 rad/s and k (wave number) is 20 rad/m. The wave speed v is given by v = ω/k, which calculates to 5 m/s.

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