Wave travel time

A plane wave has an amplitude u0 = 40 cm and a frequency f = 10 Hz. The speed of wave propagation through the medium is v = 40 cm/s. At a distance x = 10 cm from the starting point, the wave has an instantaneous deflection u = 15 cm. How long does it take for the wave to travel this path?

Final Answer:

t =  0.35 s

Step-by-step explanation:

$$\begin{gathered} u_0=40\text{cm}\to \text{m}=40:100\text{m}=0.4\text{m} \\ f=10\text{Hz} \\ v=0.40\text{m/s} \\ \omega =2\pi \cdot f=2\cdot 3.1416\cdot 10\doteq 62.83191\text{/rad} \\ s=10\text{cm}\to \text{m}=10:100\text{m}=0.1\text{m} \\ \lambda =v/f=0.4/10=\frac{1}{25}=0.04\text{m} \\ {s}_0=s+\lambda =0.1+0.04=\frac{7}{50}=0.14\text{m} \\ t=s_0/v=0.14/0.4=0.35\text{s} \end{gathered}$$

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