Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 1 / 40C / b

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- Solution b

Solution

With the convention

p = Re (p e^{iω t})

, a wave travelling in the positive

x

-direction has

p (x) = P e^{- ik x}, k = ω / c_{0} .

The linearized momentum equation gives

u = \frac{p}{ρ _{0} c _{0}}

for this right-moving wave; the sign is reversed for a left-moving wave.

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