Past exam of the mathematical methods II course of the University of Oxford / 2016 resit / 10 / b

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- Solution b

Solution

The wave speed is

c = T / ρ = 50 m s^{- 1}

, so the frequency is

f = c / λ = 100 Hz

and

ω = 200 π s^{- 1}

. Substituting the amplitude in metres,

\overline{P} = \frac{1}{2} (50) (0.1) (0.005)^{2} (200 π)^{2} = 2.5 π^{2} W ≃ 24.67 W .

Power scales with the square of amplitude; converting millimetres to metres before squaring is essential.

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